## Helton, John William

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 Author ID: helton.john-william Published as: Helton, J. William; Helton, J. W.; Helton, William J.; Helton, William; Helton, John William; Helton, J. William.; Helton, Bill; Helton, J. Homepage: https://www.math.ucsd.edu/~helton/ External Links: MGP · Wikidata · dblp · GND
 Documents Indexed: 181 Publications since 1970, including 5 Books 9 Contributions as Editor · 1 Further Contribution Biographic References: 3 Publications Co-Authors: 107 Co-Authors with 165 Joint Publications 2,401 Co-Co-Authors
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### Co-Authors

 26 single-authored 38 McCullough, Scott A. 35 Ball, Joseph Anthony 23 Klep, Igor 12 Merino, Orlando 10 Rodman, Leiba X. 9 Dym, Harry 8 Putinar, Mihai 6 Nie, Jiawang 5 Vinnikov, Victor L. 5 Volčič, Jurij 4 Evert, Eric 4 Howe, Roger Evans 4 James, Matthew R. 4 Nelson, Christopher S. 4 Stankus, Mark 4 Walker, Michael Louis 3 Cimprič, Jaka 3 Foiaş, Ciprian Ilie 3 Spitkovsky, Ilya Matvey 3 Tannenbaum, Allen Robert 3 Walker, Trent E. 3 Woerdeman, Hugo Jan 3 Zhan, Wei 2 Agler, Jim 2 Bailey, Fredric N. 2 Bolotnikov, Vladimir 2 Camino, Juan F. 2 Curto, Raúl Enrique 2 de Oliveira, Maurício Carvalho 2 Francis, Bruce Allen 2 Greene, Jeremy M. 2 Klaus, Martin 2 McEneaney, William “Mac” M. 2 Schwartz, David F. 2 Skelton, Robert E. 2 Speicher, Roland 2 Tang, Xiang 2 Wavrik, John J. 2 Williams, Ruth J. 2 Young, Nicholas John 2 Yu, Guoliang 2 Zames, George 1 Augat, Meric L. 1 Auslander, Louis 1 Basor, Estelle L. 1 Baum, Paul Frank 1 Ben-Artzi, Asher 1 Bender, Edward A. 1 Bowen, Ray M. 1 Brown, Larry 1 Byrnes, Christopher Ian 1 Coburn, Lewis A. 1 Connes, Alain 1 Craciun, Gheorghe 1 Dell Kronewitter, F. 1 Douglas, Michael R. 1 Douglas, Ronald George 1 Eidelman, Yuli 1 Evans, John W. 1 Far, Reza Rashidi 1 Gohberg, Israel 1 Gomez, Raul 1 Grudsky, Sergei Mikhailovich 1 Grünbaum, Francisco Alberto 1 Hay, Damon M. 1 Helton, F. Joanne 1 Hernandez, Joshua A. 1 Huang, Shiyuan 1 Hutchins, Shana 1 Jonckheere, Edmond A. 1 Kailath, Thomas 1 Kaminker, Jerome 1 Katsnelson, Vitaly 1 Kelly, Frank P. 1 Khargoneka, P. 1 Lam, Daniel 1 Lasserre, Jean-Bernard 1 Lewis, Albert C. 1 Lim, Adrian P. C. 1 Lin, Huaxin 1 Mai, Tobias 1 Marshall, Donald E. 1 McAllaster, Daniel P. 1 McGown, Kevin J. 1 Meier, Caleb 1 Meyer, Kyle P. 1 Misra, Gadadhar 1 Olshevsky, Vadim 1 Palmer, John N. 1 Pascoe, James Eldred 1 Paulsen, Vern Ival 1 Pierce, Stephen J. 1 Quiroga-Barranco, Raul 1 Ralston, James V. 1 Richmond, L. Bruce 1 Rosenthal, Joachim 1 Rovnyak, James 1 Sakhnovych, Lev Aronovych 1 Satriano, Matthew 1 Schweighofer, Markus ...and 19 more Co-Authors
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### Serials

 13 Journal of Functional Analysis 12 Integral Equations and Operator Theory 10 IEEE Transactions on Automatic Control 9 Indiana University Mathematics Journal 7 International Journal of Robust and Nonlinear Control 7 Operator Theory: Advances and Applications 4 International Journal of Control 4 Journal of Mathematical Analysis and Applications 4 Transactions of the American Mathematical Society 4 Journal of Operator Theory 4 SIAM Journal on Matrix Analysis and Applications 4 Linear Algebra and its Applications 3 SIAM Journal on Control and Optimization 3 Systems & Control Letters 2 Journal d’Analyse Mathématique 2 Mathematical Biosciences 2 Acta Scientiarum Mathematicarum 2 Advances in Mathematics 2 Mathematische Annalen 2 Mathematical Systems Theory 2 Mathematische Zeitschrift 2 Michigan Mathematical Journal 2 Complex Variables. Theory and Application 2 MCSS. Mathematics of Control, Signals, and Systems 2 IMRN. International Mathematics Research Notices 2 Mathematical Programming. Series A. Series B 2 SIAM Journal on Optimization 2 Annals of Mathematics. Second Series 2 Foundations of Computational Mathematics 1 Communications on Pure and Applied Mathematics 1 Linear and Multilinear Algebra 1 Rocky Mountain Journal of Mathematics 1 Acta Mathematica 1 American Journal of Mathematics 1 The Annals of Probability 1 Applied Mathematics and Optimization 1 Automatica 1 IEEE Transactions on Circuits and Systems 1 Illinois Journal of Mathematics 1 Journal of Approximation Theory 1 Journal of Differential Equations 1 Journal of Optimization Theory and Applications 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Memoirs of the American Mathematical Society 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Analysis 1 Physica D 1 International Journal of Algebra and Computation 1 The Journal of Geometric Analysis 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 Notices of the American Mathematical Society 1 Journal of Mathematical Systems, Estimation, and Control 1 The Electronic Journal of Combinatorics 1 The New York Journal of Mathematics 1 Journal of Convex Analysis 1 ELA. The Electronic Journal of Linear Algebra 1 Journal of Mathematical Chemistry 1 Positivity 1 Journal of the European Mathematical Society (JEMS) 1 IEEE Transactions on Antennas and Propagation 1 Bulletin of the American Mathematical Society 1 The IMA Volumes in Mathematics and its Applications 1 Regional Conference Series in Mathematics 1 Advances in Design and Control 1 Operators and Matrices
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### Fields

 89 Operator theory (47-XX) 64 Systems theory; control (93-XX) 41 Functional analysis (46-XX) 39 Linear and multilinear algebra; matrix theory (15-XX) 30 Algebraic geometry (14-XX) 21 Operations research, mathematical programming (90-XX) 18 Functions of a complex variable (30-XX) 15 Commutative algebra (13-XX) 14 Several complex variables and analytic spaces (32-XX) 11 Associative rings and algebras (16-XX) 10 Calculus of variations and optimal control; optimization (49-XX) 10 Numerical analysis (65-XX) 9 General and overarching topics; collections (00-XX) 8 Convex and discrete geometry (52-XX) 6 Topological groups, Lie groups (22-XX) 6 Approximations and expansions (41-XX) 6 Information and communication theory, circuits (94-XX) 5 Combinatorics (05-XX) 5 Real functions (26-XX) 5 Probability theory and stochastic processes (60-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Computer science (68-XX) 3 Field theory and polynomials (12-XX) 3 Partial differential equations (35-XX) 3 Integral transforms, operational calculus (44-XX) 3 Integral equations (45-XX) 3 Quantum theory (81-XX) 3 Biology and other natural sciences (92-XX) 2 Number theory (11-XX) 2 Special functions (33-XX) 2 Ordinary differential equations (34-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Optics, electromagnetic theory (78-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 History and biography (01-XX) 1 General algebraic systems (08-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX)

### Citations contained in zbMATH Open

149 Publications have been cited 2,016 times in 1,247 Documents Cited by Year
Linear matrix inequality representation of sets. Zbl 1116.15016
Helton, J. William; Vinnikov, Victor
2007
A Beurling-Lax theorem for the Lie group U(m,n) which contains most classical interpolation theory. Zbl 0505.47029
Ball, Joseph A.; Helton, J. William
1983
$$H^ \infty$$ control for nonlinear systems with output feedback. Zbl 0782.93032
Ball, Joseph A.; Helton, J. William; Walker, Michael L.
1993
Semidefinite representation of convex sets. Zbl 1192.90143
Helton, J. William; Nie, Jiawang
2010
“Positive” noncommutative polynomials are sums of squares. Zbl 1033.12001
Helton, J. William
2002
Noncommutative convexity arises from linear matrix inequalities. Zbl 1135.47005
Helton, J. William; McCullough, Scott A.; Vinnikov, Victor
2006
$${\mathcal H}^{\infty}$$-optimal feedback controllers for linear multivariable systems. Zbl 0572.93021
Francis, Bruce A.; Helton, J. William; Zames, George
1984
A positivstellensatz for non-commutative polynomials. Zbl 1071.47005
Helton, J. William; McCullough, Scott A.
2004
Every convex free basic semi-algebraic set has an LMI representation. Zbl 1260.14011
Helton, J. William; McCullough, Scott
2012
Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: Parametrization of the set of all solutions. Zbl 0588.47019
Ball, Joseph A.; Helton, J. William
1986
Traces of commutators of integral operators. Zbl 0332.47010
Helton, J. William; Howe, Roger E.
1975
Discrete time systems, operator models, and scattering theory. Zbl 0282.93033
Helton, J. William
1974
Sufficient and necessary conditions for semidefinite representability of convex hulls and sets. Zbl 1190.14058
Helton, J. William; Nie, Jiawang
2009
Integral operators: traces, index, and homology. Zbl 0268.47054
Helton, J. William; Howe, Roger E.
1973
The matricial relaxation of a linear matrix inequality. Zbl 1272.15012
Helton, J. William; Klep, Igor; McCullough, Scott
2013
Positive semidefinite matrices with a given sparsity pattern. Zbl 0655.15016
Agler, Jim; Helton, William; McCullough, Scott; Rodman, Leiba
1988
Operator-valued semicircular elements: solving a quadratic matrix equation with positivity constraints. Zbl 1139.15006
Helton, J. William; Far, Reza Rashidi; Speicher, Roland
2007
Extending $$H^\infty$$ control to nonlinear systems. Control of nonlinear systems to achieve performance objectives. Zbl 0941.93003
Helton, J. William; James, Matthew R.
1999
Proper analytic free maps. Zbl 1215.47011
Helton, J. William; Klep, Igor; McCullough, Scott
2011
Infinite dimensional Jordan operators and Sturm-Liouville conjugate point theory. Zbl 0251.47031
Helton, J. William
1972
A semidefinite approach for truncated $$K$$-moment problems. Zbl 1259.44005
Helton, J. William; Nie, Jiawang
2012
Inner dilations of analytic matrix functions and Darlington synthesis. Zbl 0267.30032
Douglas, R. G.; Helton, J. William
1973
Operator theory, analytic functions, matrices, and electrical engineering. Zbl 0639.47001
Helton, J. William
1987
Engineering systems and free-semi-algebraic geometry. Zbl 1156.14331
de Oliveira, Mauricio; Helton, J. William; Mccullough, Scott A.; Putinar, Mihai
2009
The convex Positivstellensatz in a free algebra. Zbl 1260.14071
Helton, J. William; Klep, Igor; McCullough, Scott
2012
Classification of hereditary matrices. Zbl 0939.47014
Agler, Jim; Helton, J. William; Stankus, Mark
1998
Worst case analysis in the frequency domain: The $$H^{\infty}$$ approach to control. Zbl 0647.93010
Helton, J. William
1985
Applications of realizations (aka linearizations) to free probability. Zbl 1376.81026
Helton, J. William; Mai, Tobias; Speicher, Roland
2018
Noncommutative ball maps. Zbl 1179.47012
Helton, J. William; Klep, Igor; McCullough, Scott; Slinglend, Nick
2009
Convex noncommutative polynomials have degree two or less. Zbl 1102.47009
Helton, J. William; McCullough, Scott
2004
Matrix inequalities: A symbolic procedure to determine convexity automatically. Zbl 1046.68139
Camino, Juan F.; Helton, J. W.; Skelton, Robert E.; Ye, Jieping
2003
The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra. Zbl 1457.14123
Helton, J. William; Klep, Igor; McCullough, Scott
2017
Non-Euclidean functional analysis and electronics. Zbl 0493.46047
Helton, J. William
1982
The possible shapes of numerical ranges. Zbl 1270.15014
Helton, J. William; Spitkovsky, I. M.
2012
Power spectrum reduction by optimal Hankel norm approximation of the phase of the outer spectral factor. Zbl 0578.93055
Jonckheere, Edmond A.; Helton, J. William
1985
Signature preserving linear maps of Hermitian matrices. Zbl 0557.15011
Helton, J. W.; Rodman, Leiba
1985
Beurling-Lax representations using classical Lie groups with many applications. III: Groups preserving two bilinear forms. Zbl 0601.47015
Ball, Joseph A.; Helton, J. William
1986
Homotopy methods for counting reaction network equilibria. Zbl 1153.92015
Craciun, Gheorghe; Helton, J. William; Williams, Ruth J.
2008
Positive polynomials in scalar and matrix variables, the spectral theorem, and optimization. Zbl 1199.47001
Helton, J. William; Putinar, Mihai
2007
A factorization principle for stabilization of linear control systems. Zbl 0759.93065
Ball, Joseph A.; Helton, J. William; Verma, Madanpal
1991
Convex matrix inequalities versus linear matrix inequalities. Zbl 1367.52007
Helton, J. William; McCullough, Scott; Putinar, Mihai; Vinnikov, Victor
2009
The distance of a function to $$H^\infty$$ in the Poincaré metric; electrical power transfer. Zbl 0496.47026
Helton, J. William
1980
Analytic mappings between noncommutative pencil balls. Zbl 1210.47039
Helton, J. William; Klep, Igor; McCullough, Scott
2011
The characteristic functions of operator theory and electrical network realization. Zbl 0246.47019
Helton, J. William
1972
The ranks of extremal positive semidefinite matrices with given sparsity pattern. Zbl 0726.05054
Helton, J. W.; Pierce, S.; Rodman, Leiba
1989
A non-commutative Positivstellensatz on isometries. Zbl 1039.47004
Helton, J. William; McCullough, Scott A.; Putinar, Mihai
2004
Free convex algebraic geometry. Zbl 1360.14008
Helton, William; Klep, Igor; McCullough, Scott
2013
Broadbanding: Gain equalization directly from data. Zbl 0481.94001
Helton, J. William
1981
A new proof of the Szegö limit theorem and new results for Toeplitz operators with discontinuous symbol. Zbl 0439.47023
Basor, E.; Helton, J. William
1980
Unitary operators on a space with an indefinite inner product. Zbl 0206.44001
Helton, J. W.
1970
Extreme points of matrix convex sets, free spectrahedra, and dilation theory. Zbl 06902272
Evert, Eric; Helton, J. William; Klep, Igor; McCullough, Scott
2018
Optimization over spaces of analytic functions and the Corona problem. Zbl 0605.46043
Helton, J. William
1986
Dilations, linear matrix inequalities, the matrix cube problem and beta distributions. Zbl 1447.47009
Helton, J. William; Klep, Igor; McCullough, Scott; Schweighofer, Markus
2019
Nonnormal dilations, disconjugacy and constrained spectral factorization. Zbl 0443.47008
Ball, Joseph A.; Helton, J. William
1980
Strong majorization in a free $$*$$-algebra. Zbl 1117.47010
Helton, J. William.; McCullough, Scott; Putinar, Mihai
2007
Beurling-Lax representations using classical Lie groups with many applications. II: $$\mathrm{GL}(n,\mathbb C)$$ and Wiener-Hopf factorization. Zbl 0539.47010
Ball, Joseph A.; Helton, William J.
1984
The first variation of the scattering matrix. Zbl 0343.35069
Helton, J. W.; Ralston, J. V.
1976
A noncommutative real nullstellensatz corresponds to a noncommutative real ideal: algorithms. Zbl 1270.14029
Cimprič, Jakob; Helton, J. William; McCullough, Scott; Nelson, Christopher
2013
Matrix convex hulls of free semialgebraic sets. Zbl 1361.46056
Helton, J. William; Klep, Igor; McCullough, Scott
2016
Geometry of free loci and factorization of noncommutative polynomials. Zbl 1420.16015
Helton, J. William; Klep, Igor; Volčič, Jurij
2018
A bang-bang theorem for optimization over spaces of analytic functions. Zbl 0589.49004
Helton, J. William; Howe, Roger E.
1986
Factorization results related to shifts in an indefinite metric. Zbl 0499.47013
Ball, Joseph A.; Helton, J. William
1982
Computer simplification of formulas in linear systems theory. Zbl 0919.93029
Helton, J. William; Stankus, Mark; Wavrik, John J.
1998
A spectral factorization approach to the distributed stable regular problem; the algebraic Riccati equation. Zbl 0343.93046
Helton, J. William
1976
Matrix extensions and eigenvalue completions, the generic case. Zbl 0891.15004
Helton, William; Rosenthal, Joachim; Wang, Xiaochang
1997
Frequency domain design and analytic selections. Zbl 0719.93017
Helton, J. William; Marshall, Donald E.
1990
Frequency response algorithms for $$H_{\infty}$$ optimization with time domain constraints. Zbl 0676.93006
Helton, J. William; Sideris, Athanasios
1989
Classical control using $$H^{\infty}$$ methods. Theory, optimization, and design. Zbl 0908.93002
Helton, J. William; Merino, Orlando
1998
Non-commutative partial matrix convexity. Zbl 1171.15020
Hay, Damon M.; Helton, J. William; Lim, Adrian; McCullough, Scott
2008
Irreducible noncommutative defining polynomials for convex sets have degree four or less. Zbl 1128.47020
Dym, Harry; Helton, William; McCullough, Scott
2007
Shift invariant manifolds and nonlinear analytic function theory. Zbl 0659.47004
Ball, Joseph A.; Helton, J. William
1988
An operator algebra approach to partial differential equations; propagation of singularities and spectral theory. Zbl 0373.35060
Helton, J. William
1977
Computer assistance for “discovering” formulas in system engineering and operator theory. Zbl 0924.93011
Helton, J. William; Stankus, Mark
1999
Jordan operators in infinite dimensions and Sturm Liouville conjugate point theory. Zbl 0234.47031
Helton, J. William
1972
On a local nonlinear commutant lifting theorems. Zbl 0652.47004
Ball, Joseph A.; Foias, Ciprian; Helton, J. William; Tannenbaum, Allen
1987
Noncommutative polynomials nonnegative on a variety intersect a convex set. Zbl 1327.13090
Helton, J. William; Klep, Igor; Nelson, Christopher S.
2014
Algebras, synchronous games, and chromatic numbers of graphs. Zbl 1410.05069
Helton, J. William; Meyer, Kyle P.; Paulsen, Vern I.; Satriano, Matthew
2019
Bianalytic maps between free spectrahedra. Zbl 1471.47045
Augat, Meric; Helton, J. William; Klep, Igor; McCullough, Scott
2018
Arveson extreme points span free spectrahedra. Zbl 1440.47056
Evert, Eric; Helton, J. William
2019
Lie groups over the field of rational functions, signed spectral factorization, signed interpolation, and amplifier design. Zbl 0493.22008
Ball, Joseph A.; Helton, J. William
1982
$$H^{\infty}$$-optimal feedback controllers for linear multivariable systems. Zbl 0552.93040
Francis, B. A.; Helton, J. W.; Zames, G.
1984
Rules for computer simplification of the formulas in operator model theory and linear systems. Zbl 0876.47012
Helton, J. William; Wavrik, John J.
1994
Nonlinear $$H^ \infty$$ control theory for stable plants. Zbl 0760.93021
Ball, Joseph A.; Helton, J. William
1992
Viscosity solutions of Hamilton-Jacobi equations arising in nonlinear $$H_ \infty$$-control. Zbl 0844.93035
Ball, Joseph A.; Helton, J. William
1996
Dissipative control systems synthesis with full state feedback. Zbl 0929.93014
Yuliar, S.; James, M. R.; Helton, J. W.
1998
Determinant expansions of signed matrices and of certain Jacobians. Zbl 1191.15023
Helton, J. William; Klep, Igor; Gomez, Raul
2009
Operators unitary in an indefinite metric and linear fractional transformations. Zbl 0225.47025
Helton, J. William
1971
Non-negative hereditary polynomials in a free $$*$$-algebra. Zbl 1103.47012
Helton, J. William; McCullough, Scott A.; Putinar, Mihai
2005
Free analysis, convexity and LMI domains. Zbl 1280.46043
Helton, J. William; Klep, Igor; McCullough, Scott
2012
Interpolation with outer functions and gain equalization in amplifiers. Zbl 0498.94014
Ball, Joseph A.; Helton, William J.
1979
Inner-outer factorization of nonlinear operators. Zbl 0762.93039
Ball, Joseph A.; Helton, J. William
1992
Manipulating matrix inequalities automatically. Zbl 1050.15021
Helton, J. William
2003
Beurling-Lax representations using classical Lie groups with many applications. IV. GL(n,R), $$U^ *(2n)$$, SL(n,$${\mathbb{C}})$$, and a solvable group. Zbl 0614.47003
Ball, Joseph A.; Helton, J. William
1986
Conditions for optimality over $$H^ \infty$$. Zbl 0794.49022
Helton, J. William; Merino, Orlando
1993
Algorithms for optimizing over analytic functions. Zbl 0792.65039
Helton, J. W.; Merino, O.; Walker, T. E.
1993
Noncommutative plurisubharmonic polynomials. I: Global assumptions. Zbl 1254.47005
Greene, Jeremy M.; Helton, J. William; Vinnikov, Victor
2011
Asymptotics of permutations with nearly periodic patterns of rises and falls. Zbl 1031.05015
Bender, Edward A.; Helton, William J.; Richmond, L. Bruce
2003
Computer algebra tailored to matrix inequalities in control. Zbl 1133.93333
de Oliveira, M. C.; Helton, J. W.
2006
Nonlinear $$H^{\infty}$$-control theory: A literature survey. Zbl 0733.93019
Ball, Joseph A.; Helton, J. William
1990
The Hessian of a noncommutative polynomial has numerous negative eigenvalues. Zbl 1143.47004
Dym, Harry; Helton, J. William; McCullough, Scott
2007
Noncommutative polynomials describing convex sets. Zbl 1471.14120
Helton, J. William; Klep, Igor; McCullough, Scott; Volčič, Jurij
2021
Bianalytic free maps between spectrahedra and spectraballs. Zbl 1445.47052
Helton, J. William; Klep, Igor; McCullough, Scott; Volčič, Jurij
2020
Dilations, linear matrix inequalities, the matrix cube problem and beta distributions. Zbl 1447.47009
Helton, J. William; Klep, Igor; McCullough, Scott; Schweighofer, Markus
2019
Algebras, synchronous games, and chromatic numbers of graphs. Zbl 1410.05069
Helton, J. William; Meyer, Kyle P.; Paulsen, Vern I.; Satriano, Matthew
2019
Arveson extreme points span free spectrahedra. Zbl 1440.47056
Evert, Eric; Helton, J. William
2019
Ronald G. Douglas: a master in the art of transcending problems. Zbl 1427.01030
Yu, Guoliang; Howe, Roger; Hutchins, Shana
2019
Applications of realizations (aka linearizations) to free probability. Zbl 1376.81026
Helton, J. William; Mai, Tobias; Speicher, Roland
2018
Extreme points of matrix convex sets, free spectrahedra, and dilation theory. Zbl 06902272
Evert, Eric; Helton, J. William; Klep, Igor; McCullough, Scott
2018
Geometry of free loci and factorization of noncommutative polynomials. Zbl 1420.16015
Helton, J. William; Klep, Igor; Volčič, Jurij
2018
Bianalytic maps between free spectrahedra. Zbl 1471.47045
Augat, Meric; Helton, J. William; Klep, Igor; McCullough, Scott
2018
The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra. Zbl 1457.14123
Helton, J. William; Klep, Igor; McCullough, Scott
2017
Circular free spectrahedra. Zbl 1351.15011
Evert, Eric; Helton, J. William; Klep, Igor; McCullough, Scott
2017
Non-commutative polynomials with convex level slices. Zbl 1402.15011
Dym, Harry; Helton, John William; McCullough, Scott
2017
Matrix convex hulls of free semialgebraic sets. Zbl 1361.46056
Helton, J. William; Klep, Igor; McCullough, Scott
2016
Convex entire noncommutative functions are polynomials of degree two or less. Zbl 1369.47014
Helton, J. William; Pascoe, J. E.; Tully-Doyle, Ryan; Vinnikov, Victor
2016
Free semidefinite representation of matrix power functions. Zbl 1307.90130
Helton, J. William; Nie, Jiawang; Semko, Jeremy S.
2015
Real Nullstellensatz and *-ideals in *-algebras. Zbl 1332.13020
Cimpric, J.; Helton, J. W.; McCullough, S.; Nelson, C.
2015
Noncommutative polynomials nonnegative on a variety intersect a convex set. Zbl 1327.13090
Helton, J. William; Klep, Igor; Nelson, Christopher S.
2014
Free convex sets defined by rational expressions have LMI representations. Zbl 1298.47025
Helton, J. William; McCullough, Scott
2014
On real one-sided ideals in a free algebra. Zbl 1283.14025
Cimprič, Jakob; Helton, J. William; Klep, Igor; McCullough, Scott; Nelson, Christopher
2014
The matricial relaxation of a linear matrix inequality. Zbl 1272.15012
Helton, J. William; Klep, Igor; McCullough, Scott
2013
Free convex algebraic geometry. Zbl 1360.14008
Helton, William; Klep, Igor; McCullough, Scott
2013
A noncommutative real nullstellensatz corresponds to a noncommutative real ideal: algorithms. Zbl 1270.14029
Cimprič, Jakob; Helton, J. William; McCullough, Scott; Nelson, Christopher
2013
Every convex free basic semi-algebraic set has an LMI representation. Zbl 1260.14011
Helton, J. William; McCullough, Scott
2012
A semidefinite approach for truncated $$K$$-moment problems. Zbl 1259.44005
Helton, J. William; Nie, Jiawang
2012
The convex Positivstellensatz in a free algebra. Zbl 1260.14071
Helton, J. William; Klep, Igor; McCullough, Scott
2012
The possible shapes of numerical ranges. Zbl 1270.15014
Helton, J. William; Spitkovsky, I. M.
2012
Free analysis, convexity and LMI domains. Zbl 1280.46043
Helton, J. William; Klep, Igor; McCullough, Scott
2012
Semidefinite representation of convex sets and convex hulls. Zbl 1334.90104
Helton, J. William; Nie, Jiawang
2012
Convexity and semidefinite programming in dimension-free matrix unknowns. Zbl 1334.90103
Helton, J. William; Klep, Igor; Mccullough, Scott
2012
Proper analytic free maps. Zbl 1215.47011
Helton, J. William; Klep, Igor; McCullough, Scott
2011
Analytic mappings between noncommutative pencil balls. Zbl 1210.47039
Helton, J. William; Klep, Igor; McCullough, Scott
2011
Noncommutative plurisubharmonic polynomials. I: Global assumptions. Zbl 1254.47005
Greene, Jeremy M.; Helton, J. William; Vinnikov, Victor
2011
Non-commutative varieties with curvature having bounded signature. Zbl 1277.47026
Dym, Harry; Helton, J. William; McCullough, Scott
2011
Semidefinite representation of convex sets. Zbl 1192.90143
Helton, J. William; Nie, Jiawang
2010
Sign patterns for chemical reaction networks. Zbl 1197.92061
Helton, J. William; Katsnelson, Vitaly; Klep, Igor
2010
Sufficient and necessary conditions for semidefinite representability of convex hulls and sets. Zbl 1190.14058
Helton, J. William; Nie, Jiawang
2009
Engineering systems and free-semi-algebraic geometry. Zbl 1156.14331
de Oliveira, Mauricio; Helton, J. William; Mccullough, Scott A.; Putinar, Mihai
2009
Noncommutative ball maps. Zbl 1179.47012
Helton, J. William; Klep, Igor; McCullough, Scott; Slinglend, Nick
2009
Convex matrix inequalities versus linear matrix inequalities. Zbl 1367.52007
Helton, J. William; McCullough, Scott; Putinar, Mihai; Vinnikov, Victor
2009
Determinant expansions of signed matrices and of certain Jacobians. Zbl 1191.15023
Helton, J. William; Klep, Igor; Gomez, Raul
2009
Classification of all noncommutative polynomials whose Hessian has negative signature one and a noncommutative second fundamental form. Zbl 1206.47007
Dym, Harry; Greene, Jeremy M.; Helton, J. William; McCullough, Scott A.
2009
Homotopy methods for counting reaction network equilibria. Zbl 1153.92015
Craciun, Gheorghe; Helton, J. William; Williams, Ruth J.
2008
Non-commutative partial matrix convexity. Zbl 1171.15020
Hay, Damon M.; Helton, J. William; Lim, Adrian; McCullough, Scott
2008
Measures with zeros in the inverse of their moment matrix. Zbl 1169.15005
Helton, J. William; Lasserre, Jean B.; Putinar, Mihai
2008
Non-commutative harmonic and subharmonic polynomials. Zbl 1169.47007
Helton, J. William; McAllaster, Daniel P.; Hernandez, Joshua A.
2008
Linear matrix inequality representation of sets. Zbl 1116.15016
Helton, J. William; Vinnikov, Victor
2007
Operator-valued semicircular elements: solving a quadratic matrix equation with positivity constraints. Zbl 1139.15006
Helton, J. William; Far, Reza Rashidi; Speicher, Roland
2007
Positive polynomials in scalar and matrix variables, the spectral theorem, and optimization. Zbl 1199.47001
Helton, J. William; Putinar, Mihai
2007
Strong majorization in a free $$*$$-algebra. Zbl 1117.47010
Helton, J. William.; McCullough, Scott; Putinar, Mihai
2007
Irreducible noncommutative defining polynomials for convex sets have degree four or less. Zbl 1128.47020
Dym, Harry; Helton, William; McCullough, Scott
2007
The Hessian of a noncommutative polynomial has numerous negative eigenvalues. Zbl 1143.47004
Dym, Harry; Helton, J. William; McCullough, Scott
2007
Noncommutative convexity arises from linear matrix inequalities. Zbl 1135.47005
Helton, J. William; McCullough, Scott A.; Vinnikov, Victor
2006
Computer algebra tailored to matrix inequalities in control. Zbl 1133.93333
de Oliveira, M. C.; Helton, J. W.
2006
Solving matrix inequalities whose unknowns are matrices. Zbl 1112.90058
Camino, Juan F.; Helton, J. William; Skelton, Robert E.
2006
Matrix representations for positive noncommutative polynomials. Zbl 1094.47006
Helton, J. William; McCullough, Scott; Putinar, Mihai
2006
Non-negative hereditary polynomials in a free $$*$$-algebra. Zbl 1103.47012
Helton, J. William; McCullough, Scott A.; Putinar, Mihai
2005
Extremal problems of interpolation theory. Zbl 1094.47026
Helton, J. William; Sakhnovich, L. A.
2005
A positivstellensatz for non-commutative polynomials. Zbl 1071.47005
Helton, J. William; McCullough, Scott A.
2004
Convex noncommutative polynomials have degree two or less. Zbl 1102.47009
Helton, J. William; McCullough, Scott
2004
A non-commutative Positivstellensatz on isometries. Zbl 1039.47004
Helton, J. William; McCullough, Scott A.; Putinar, Mihai
2004
Matrix inequalities: A symbolic procedure to determine convexity automatically. Zbl 1046.68139
Camino, Juan F.; Helton, J. W.; Skelton, Robert E.; Ye, Jieping
2003
Manipulating matrix inequalities automatically. Zbl 1050.15021
Helton, J. William
2003
Asymptotics of permutations with nearly periodic patterns of rises and falls. Zbl 1031.05015
Bender, Edward A.; Helton, William J.; Richmond, L. Bruce
2003
“Positive” noncommutative polynomials are sums of squares. Zbl 1033.12001
Helton, J. William
2002
Multidisk problems in $$H^{\infty}$$ optimization: A method for analysing numerical algorithms. Zbl 1044.93017
Dym, Harry; Helton, William J.; Merino, Orlando
2002
Some adaptive control problems which convert to a “classical” problem in several complex variables. Zbl 1010.93059
Helton, J. William
2001
Extending $$H^\infty$$ control to nonlinear systems. Control of nonlinear systems to achieve performance objectives. Zbl 0941.93003
Helton, J. William; James, Matthew R.
1999
Computer assistance for “discovering” formulas in system engineering and operator theory. Zbl 0924.93011
Helton, J. William; Stankus, Mark
1999
Classification of hereditary matrices. Zbl 0939.47014
Agler, Jim; Helton, J. William; Stankus, Mark
1998
Computer simplification of formulas in linear systems theory. Zbl 0919.93029
Helton, J. William; Stankus, Mark; Wavrik, John J.
1998
Classical control using $$H^{\infty}$$ methods. Theory, optimization, and design. Zbl 0908.93002
Helton, J. William; Merino, Orlando
1998
Dissipative control systems synthesis with full state feedback. Zbl 0929.93014
Yuliar, S.; James, M. R.; Helton, J. W.
1998
Classical control using $$H^{\infty}$$ methods. An introduction to design. Zbl 0908.93003
Helton, J. William; Merino, Orlando
1998
Matrix extensions and eigenvalue completions, the generic case. Zbl 0891.15004
Helton, William; Rosenthal, Joachim; Wang, Xiaochang
1997
Viscosity solutions of Hamilton-Jacobi equations arising in nonlinear $$H_ \infty$$-control. Zbl 0844.93035
Ball, Joseph A.; Helton, J. William
1996
Non-minimal factorization of nonlinear systems: The observable case. Zbl 0853.93027
Ben-Artzi, Asher; Helton, J. William; Woerdeman, Hugo J.
1996
Rules for computer simplification of the formulas in operator model theory and linear systems. Zbl 0876.47012
Helton, J. William; Wavrik, John J.
1994
A fibered polynomial hull without an analytic selection. Zbl 0811.32008
Helton, J. William; Merino, Orlando
1994
Sparsity patterns with high rank extremal positive semidefinite matrices. Zbl 0796.05065
Helton, J. William; Lam, Daniel; Woerdeman, Hugo J.
1994
$$H^ \infty$$ control for nonlinear systems with output feedback. Zbl 0782.93032
Ball, Joseph A.; Helton, J. William; Walker, Michael L.
1993
Conditions for optimality over $$H^ \infty$$. Zbl 0794.49022
Helton, J. William; Merino, Orlando
1993
Algorithms for optimizing over analytic functions. Zbl 0792.65039
Helton, J. W.; Merino, O.; Walker, T. E.
1993
Symmetric Hankel operators: Minimal norm extensions and eigenstructures. Zbl 0774.15015
Helton, J. William; Woerdeman, Hugo J.
1993
Novel approach to accelerating Newton’s method for sup-norm optimization arising in $$H^ \infty$$-control. Zbl 0794.93027
Helton, J. W.; Merino, O.
1993
Nonlinear $$H^ \infty$$ control theory for stable plants. Zbl 0760.93021
Ball, Joseph A.; Helton, J. William
1992
Inner-outer factorization of nonlinear operators. Zbl 0762.93039
Ball, Joseph A.; Helton, J. William
1992
A factorization principle for stabilization of linear control systems. Zbl 0759.93065
Ball, Joseph A.; Helton, J. William; Verma, Madanpal
1991
Tracking poles and representing Hankel operators directly from data. Zbl 0726.30003
Helton, J. W.; Spain, P. G.; Young, N. J.
1991
Frequency domain design and analytic selections. Zbl 0719.93017
Helton, J. William; Marshall, Donald E.
1990
Nonlinear $$H^{\infty}$$-control theory: A literature survey. Zbl 0733.93019
Ball, Joseph A.; Helton, J. William
1990
Approximation of Hankel operators: Truncation error in an $$H^{\infty}$$ design method. Zbl 0711.93030
Helton, J. W.; Young, N. J.
1990
Signal processing. Part II: Control theory and applications. Based on lectures held at the IMA, Minneapolis, MN (USA) from June 27 to August 5, 1988. Zbl 0691.00018
1990
The ranks of extremal positive semidefinite matrices with given sparsity pattern. Zbl 0726.05054
Helton, J. W.; Pierce, S.; Rodman, Leiba
1989
Frequency response algorithms for $$H_{\infty}$$ optimization with time domain constraints. Zbl 0676.93006
Helton, J. William; Sideris, Athanasios
1989
A Poincaré-Dulac approach to a nonlinear Beurling-Lax-Halmos theorem. Zbl 0688.47022
Ball, Joseph A.; Foias, Ciprian; Helton, J. William; Tannenbaum, Allen
1989
Interconnection of nonlinear causal systems. Zbl 0693.93035
Ball, Joseph A.; Helton, J. William
1989
Positive semidefinite matrices with a given sparsity pattern. Zbl 0655.15016
Agler, Jim; Helton, William; McCullough, Scott; Rodman, Leiba
1988
Shift invariant manifolds and nonlinear analytic function theory. Zbl 0659.47004
Ball, Joseph A.; Helton, J. William
1988
Sensitivity bandwidth optimization for nonlinear feedback systems. Zbl 0673.93017
Ball, Joseph A.; Helton, J. William
1988
...and 49 more Documents
all top 5

### Cited by 1,212 Authors

 74 Helton, John William 46 Klep, Igor 37 Ball, Joseph Anthony 36 McCullough, Scott A. 24 Alpay, Daniel Aron 24 Nakazato, Hiroshi 22 Chien, Mao-Ting 21 Vinnikov, Victor L. 19 Bolotnikov, Vladimir 19 Putinar, Mihai 17 Agler, Jim 17 Volčič, Jurij 15 Kummer, Mario Denis 15 Nie, Jiawang 14 Dym, Harry 14 Gu, Caixing 14 Krüger, Torben 14 Young, Nicholas John 13 Erdős, László 13 Jeyakumar, Vaithilingam 12 Pascoe, James Eldred 12 Spitkovsky, Ilya Matvey 11 Arov, Damir Zyamovich 11 Rodman, Leiba X. 11 Shamovich, Eli 10 Cimprič, Jaka 10 Fan, Jinyan 10 Netzer, Tim 10 Popescu, Gelu 9 Curtain, Ruth Frances 9 Gohberg, Israel 8 Frazho, Arthur E. 8 Li, Guoyin 8 Plaumann, Daniel 8 Ran, André C. M. 8 Saunderson, James 8 Stankus, Mark 8 Xia, Daoxing 7 Belinschi, Serban Teodor 7 Brändén, Petter 7 Constantinescu, Tiberiu 7 Dijksma, Aad 7 Foiaş, Ciprian Ilie 7 Fritzsche, Bernd 7 Henrion, Didier 7 Jiao, Liguo 7 Jonckheere, Edmond A. 7 Kirstein, Bernd 7 Lasserre, Jean-Bernard 7 Lee, Jae Hyoung 7 Loewy, Raphael 7 McCarthy, John Edward 7 Povh, Janez 7 Schweighofer, Markus 7 Tannenbaum, Allen Robert 7 Zhou, Anwa 6 Alt, Johannes 6 Cafuta, Kristijan 6 Chō, Muneo 6 Dey, Papri 6 Kaashoek, Marinus Adriaan 6 Nguang, Sing Kiong 6 Parrilo, Pablo A. 6 Pierce, Stephen J. 6 Scheiderer, Claus 6 Sinn, Rainer 5 Ahmadi, Amir Ali 5 Bermúdez, Teresa 5 Chen, Gongning 5 Chuong, Thai Doan 5 Evert, Eric 5 Fawzi, Hamza 5 Fuhrmann, Paul A. 5 Guillot, Dominique 5 Kaliuzhnyi-Verbovetskyi, Dmitry S. 5 Khare, Apoorva 5 Lewkowicz, Izchak 5 Li, Chi-Kwong 5 Peller, Vladimir Vsevolodovich 5 Rovnyak, James 5 Sturmfels, Bernd 5 Tadmor, Gilead 5 Theobald, Thorsten 5 Thom, Andreas Berthold 5 Verma, Madanpal S. 5 Vinzant, Cynthia 5 Wegert, Elias 5 Widom, Harold 4 Anderson, Brian David Outram 4 Başar, Tamer 4 Byrnes, Christopher Ian 4 Chen, Borsen 4 Chen, Chung-Cheng 4 Derkach, Vladimir Alexandrovich 4 Gheondea, Aurelian 4 Hu, Yongjian 4 James, Matthew R. 4 Jury, Michael T. 4 Khargonekar, Pramod P. 4 Kimura, Hidenori ...and 1,112 more Authors
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### Cited in 248 Serials

 129 Linear Algebra and its Applications 93 Integral Equations and Operator Theory 75 Journal of Functional Analysis 66 Systems & Control Letters 50 Automatica 44 International Journal of Control 43 Journal of Mathematical Analysis and Applications 31 Proceedings of the American Mathematical Society 30 Mathematical Programming. Series A. Series B 25 Transactions of the American Mathematical Society 19 Linear and Multilinear Algebra 19 Advances in Mathematics 19 Complex Analysis and Operator Theory 18 SIAM Journal on Optimization 15 MCSS. Mathematics of Control, Signals, and Systems 13 SIAM Journal on Applied Algebra and Geometry 12 Journal of Global Optimization 11 Journal of Symbolic Computation 11 International Journal of Robust and Nonlinear Control 10 Journal of Mathematical Physics 10 Journal of Optimization Theory and Applications 10 Computational Optimization and Applications 9 International Journal of Systems Science 8 Journal of Soviet Mathematics 8 Mathematische Annalen 8 Acta Applicandae Mathematicae 7 Communications in Mathematical Physics 7 Multidimensional Systems and Signal Processing 7 Foundations of Computational Mathematics 6 Journal d’Analyse Mathématique 6 Mathematische Zeitschrift 6 Circuits, Systems, and Signal Processing 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Mathematical Biosciences 5 Applied Mathematics and Computation 5 Journal of Algebra 5 Journal of Approximation Theory 5 Journal of Pure and Applied Algebra 5 Discrete & Computational Geometry 5 Communications in Partial Differential Equations 5 European Journal of Control 4 Israel Journal of Mathematics 4 Arkiv för Matematik 4 The Annals of Probability 4 Journal of Multivariate Analysis 4 Mathematical Systems Theory 4 Operations Research Letters 4 The Journal of Geometric Analysis 4 Bulletin of the American Mathematical Society. New Series 4 Bulletin des Sciences Mathématiques 4 Nonlinear Dynamics 4 Optimization Methods & Software 4 Optimization Letters 4 Banach Journal of Mathematical Analysis 3 Bulletin of the Australian Mathematical Society 3 Communications on Pure and Applied Mathematics 3 Journal of the Franklin Institute 3 Ukrainian Mathematical Journal 3 Acta Mathematica 3 Journal of Combinatorial Theory. Series A 3 Journal of Computational and Applied Mathematics 3 Journal für die Reine und Angewandte Mathematik 3 Mathematische Nachrichten 3 Memoirs of the American Mathematical Society 3 Michigan Mathematical Journal 3 Numerische Mathematik 3 Results in Mathematics 3 Probability Theory and Related Fields 3 International Journal of Adaptive Control and Signal Processing 3 Applied Mathematical Modelling 3 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques 3 Journal of Mathematical Sciences (New York) 3 Electronic Journal of Probability 3 Journal of Mathematical Chemistry 3 Mathematical Problems in Engineering 3 Journal of Vibration and Control 3 Annales Henri Poincaré 3 Computational Methods and Function Theory 3 Journal of Noncommutative Geometry 3 Operators and Matrices 3 Science China. Mathematics 3 Concrete Operators 3 International Journal of Systems Science. Principles and Applications of Systems and Integration 2 Applicable Analysis 2 Archive for Rational Mechanics and Analysis 2 Communications in Algebra 2 Journal of Statistical Physics 2 Mathematical Notes 2 Rocky Mountain Journal of Mathematics 2 Mathematics of Computation 2 Chaos, Solitons and Fractals 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Applied Mathematics and Optimization 2 Archiv der Mathematik 2 Bulletin of the London Mathematical Society 2 Duke Mathematical Journal 2 Functional Analysis and its Applications 2 Journal of Differential Equations 2 Mathematica Slovaca 2 Numerical Functional Analysis and Optimization ...and 148 more Serials
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### Cited in 57 Fields

 440 Operator theory (47-XX) 347 Systems theory; control (93-XX) 241 Linear and multilinear algebra; matrix theory (15-XX) 201 Functional analysis (46-XX) 184 Operations research, mathematical programming (90-XX) 136 Functions of a complex variable (30-XX) 129 Algebraic geometry (14-XX) 68 Numerical analysis (65-XX) 63 Convex and discrete geometry (52-XX) 60 Probability theory and stochastic processes (60-XX) 55 Several complex variables and analytic spaces (32-XX) 53 Associative rings and algebras (16-XX) 51 Commutative algebra (13-XX) 47 Combinatorics (05-XX) 42 Calculus of variations and optimal control; optimization (49-XX) 36 Partial differential equations (35-XX) 36 Quantum theory (81-XX) 31 Approximations and expansions (41-XX) 26 Number theory (11-XX) 26 Computer science (68-XX) 25 Harmonic analysis on Euclidean spaces (42-XX) 24 Field theory and polynomials (12-XX) 20 Real functions (26-XX) 20 Ordinary differential equations (34-XX) 19 Biology and other natural sciences (92-XX) 16 Integral transforms, operational calculus (44-XX) 15 Global analysis, analysis on manifolds (58-XX) 15 Information and communication theory, circuits (94-XX) 14 Dynamical systems and ergodic theory (37-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Statistics (62-XX) 12 Mechanics of particles and systems (70-XX) 10 Topological groups, Lie groups (22-XX) 9 Integral equations (45-XX) 8 General algebraic systems (08-XX) 8 $$K$$-theory (19-XX) 7 Nonassociative rings and algebras (17-XX) 7 Group theory and generalizations (20-XX) 7 Abstract harmonic analysis (43-XX) 7 Differential geometry (53-XX) 6 Mathematical logic and foundations (03-XX) 6 Category theory; homological algebra (18-XX) 5 General and overarching topics; collections (00-XX) 5 Special functions (33-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Measure and integration (28-XX) 4 Difference and functional equations (39-XX) 4 Geometry (51-XX) 4 Mechanics of deformable solids (74-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Potential theory (31-XX) 1 History and biography (01-XX) 1 Sequences, series, summability (40-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Astronomy and astrophysics (85-XX)

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