## Van Assche, Walter

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 Author ID: van-assche.walter Published as: Van Assche, Walter; Van Assche, W.; van Assche, Walter; van Assche, W.; Assche, Walter Van; Assche, W. more...less Homepage: https://www.kuleuven.be/wieiswie/en/person/00002417 External Links: MGP · ORCID · Wikidata · ResearchGate · dblp · IdRef
 Documents Indexed: 167 Publications since 1982, including 2 Books 12 Contributions as Editor · 5 Further Contributions Reviewing Activity: 167 Reviews Co-Authors: 106 Co-Authors with 139 Joint Publications 2,355 Co-Co-Authors
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### Co-Authors

 43 single-authored 12 Aptekarev, Alexander Ivanovich 12 Geronimo, Jeffrey S. 12 Kuijlaars, Arno B. J. 10 Filipuk, Galina V. 8 Coussement, Jonathan 7 Nevai, Paul G. 5 Boelen, Lies 5 Coussement, Els 5 Dehesa, Jesús S. 5 Ismail, Mourad El-Houssieny 5 Marcellán Español, Francisco 5 Smet, Christophe 4 Yáñez, Rafael J. 4 Zhang, Lun 3 Derevyagin, Maxim S. 3 Koelink, Erik 3 Martínez-Finkelshtein, Andrei 3 Ndayiragije, François 3 Wielonsky, Franck 2 Bultheel, Adhemar François 2 Buyarov, V. S. 2 Daruis, Leyla 2 Delbeke, Lieve 2 Golinskii, Leonid Borisovich 2 González-Férez, Rosario 2 Haneczok, Maciej 2 Koornwinder, Tom H. 2 Lenin, R. B. 2 Leurs, Marjolein 2 López Lagomasino, Guillermo Tomás 2 Loureiro, Ana Filipa 2 Njåstad, Olav 2 Parthasarathy, Panamalai Ramarao 2 Postelmans, Kelly 2 Ranga, A. Sri 2 Schoutens, Wim 2 Sinap, Ann 2 Stahl, Herbert Robert 2 Teugels, Jozef L. 2 Van Barel, Marc 2 Vanden Berghe, Guido 1 Alfaro García, Manuel 1 Alsulami, Saud Mastour A. 1 Álvarez-Nodarse, Renato 1 Arvesú, Jorge 1 Askey, Richard Allen 1 Beckermann, Bernhard 1 Beirlant, Jan 1 Bessis, Daniel 1 Beukers, Frits 1 Branquinho, Amílcar José Pinto Lopes 1 Brezinski, Claude 1 Bruno, Oscar P. 1 Carbonez, An 1 Chen, Yang 1 Clarkson, Peter A. 1 Cushing, Jim M. 1 Cuyt, Annie A. M. 1 de Andrade, Eliana X. L. 1 Dimitrov, Dimitar K. 1 Dominici, Diego Ernesto 1 Dresse, Zoé 1 Durán, Antonio José 1 Elaydi, Saber Nasr 1 Fano, Guido 1 Foupouagnigni, Mama 1 Gautschi, Walter 1 Gawronski, Wolfgang 1 González-Vera, Pablo 1 Goossens, Marcel 1 Harrell, Evans M. II 1 Iliev, Plamen 1 Jones, William Branham 1 Kaliaguine, Valeri A. 1 Kanemitsu, Shigeru 1 Korevaar, Jacob 1 Koutschan, Christoph 1 Lasser, Rupert 1 Levrie, Paul 1 López-Artés, P. 1 Lubinsky, Doron S. 1 Luxemburg, Wilhelmus Anthonius Josephus 1 Maejima, Makoto 1 Magnus, Alphonse Ph. 1 Máté, Attila 1 McLaughlin, Kenneth D. T.-R. 1 Miki, Hiroshi 1 Milovanović, Gradimir V. 1 Mínguez Ceniceros, Judit 1 Monegato, Giovanni 1 Neuschel, Thorsten 1 Nuwacu, Jean Paul 1 Ortolani, Fabio 1 Papageorgiou, Vassilios G. 1 Pintér, Ferenc 1 Reichel, Lothar 1 Ronveaux, André 1 Ruffing, Andreas 1 Sameh, Ahmed H. 1 Smith, Dale T. ...and 18 more Co-Authors
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### Serials

 31 Journal of Approximation Theory 21 Journal of Computational and Applied Mathematics 11 Constructive Approximation 9 Proceedings of the American Mathematical Society 5 Journal of Physics A: Mathematical and Theoretical 4 Journal of Mathematical Analysis and Applications 4 Rocky Mountain Journal of Mathematics 4 Transactions of the American Mathematical Society 4 Journal of Physics A: Mathematical and General 4 SIAM Journal on Mathematical Analysis 4 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Journal of Mathematical Physics 3 Journal of Difference Equations and Applications 3 Lecture Notes in Mathematics 2 Inverse Problems 2 Linear Algebra and its Applications 2 ETNA. Electronic Transactions on Numerical Analysis 2 Methods and Applications of Analysis 2 Integral Transforms and Special Functions 2 Analysis and Applications (Singapore) 2 Encyclopedia of Mathematics and Its Applications 1 Astronomy and Astrophysics 1 Communications on Pure and Applied Mathematics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Nonlinearity 1 Revue Roumaine de Mathématiques Pures et Appliquées 1 Mathematics of Computation 1 Acta Arithmetica 1 Advances in Mathematics 1 Journal of Applied Probability 1 Journal of Number Theory 1 The Mathematical Scientist 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Sankhyā. Series A. Methods and Techniques 1 Bulletin de la Société Matheḿatique de Belgique. Série B 1 Advances in Applied Mathematics 1 Physica D 1 Sequential Analysis 1 Numerical Algorithms 1 Notices of the American Mathematical Society 1 Indagationes Mathematicae. New Series 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Sbornik: Mathematics 1 Doklady Mathematics 1 The Ramanujan Journal 1 Journal of Nonlinear Mathematical Physics 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Computational Methods and Function Theory 1 IMRP. International Mathematics Research Papers 1 Surveys in Approximation Theory (SAT) 1 Australian Mathematical Society Lecture Series 1 Jaen Journal on Approximation 1 Contemporary Mathematicians
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### Fields

 113 Special functions (33-XX) 110 Harmonic analysis on Euclidean spaces (42-XX) 41 Approximations and expansions (41-XX) 20 Functions of a complex variable (30-XX) 20 Difference and functional equations (39-XX) 14 Numerical analysis (65-XX) 13 Ordinary differential equations (34-XX) 12 Operator theory (47-XX) 11 General and overarching topics; collections (00-XX) 11 Number theory (11-XX) 9 Probability theory and stochastic processes (60-XX) 8 Dynamical systems and ergodic theory (37-XX) 7 History and biography (01-XX) 7 Potential theory (31-XX) 7 Partial differential equations (35-XX) 7 Information and communication theory, circuits (94-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Statistics (62-XX) 6 Quantum theory (81-XX) 5 Real functions (26-XX) 5 Sequences, series, summability (40-XX) 2 Mechanics of deformable solids (74-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Topological groups, Lie groups (22-XX) 1 Integral transforms, operational calculus (44-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

156 Publications have been cited 2,603 times in 1,250 Documents Cited by Year
Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Zbl 1082.42016
2005
The Riemann–Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]. Zbl 1082.42017
Kuijlaars, A. B. J.; Mclaughlin, K. T.-R.; Van Assche, W.; Vanlessen, M.
2004
Orthogonal matrix polynomials and higher-order recurrence relations. Zbl 0827.15027
Durán, A. J.; Van Assche, Walter
1995
Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Paperback reprint of the 2005 original. Zbl 1172.42008
2009
Multiple orthogonal polynomials for classical weights. Zbl 1033.33002
Aptekarev, A. I.; Branquinho, A.; Van Assche, W.
2003
Some classical multiple orthogonal polynomials. Zbl 0969.33005
Van Assche, Walter; Coussement, Els
2001
Asymptotics for orthogonal polynomials. Zbl 0617.42014
Van Assche, Walter
1987
Orthogonal polynomials on several intervals via a polynomial mapping. Zbl 0652.42009
Geronimo, J. S.; Van Assche, Walter
1988
Riemann-Hilbert problems for multiple orthogonal polynomials. Zbl 0997.42012
Van Assche, Walter; Geronimo, Jeffrey S.; Kuijlaars, Arno B. J.
2001
The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients. Zbl 0967.33009
Kuijlaars, A. B. J.; Van Assche, W.
1999
Orthogonal matrix polynomials and applications. Zbl 0863.42018
Sinap, Ann; Van Assche, Walter
1996
Orthogonal polynomials with asymptotically periodic recurrent coefficients. Zbl 0604.42023
Geronimo, J. S.; Van Assche, Walter
1986
Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner product. Zbl 0840.42017
López, G.; Marcellán, F.; Van Assche, Walter
1995
Some discrete multiple orthogonal polynomials. Zbl 1021.33006
Arvesú, J.; Coussement, J.; Van Assche, W.
2003
Multiple orthogonal polynomials associated with Macdonald functions. Zbl 0959.42016
Van Assche, W.; Yakubovich, S. B.
2000
Orthogonal polynomials, associated polynomials and functions of the second kind. Zbl 0744.42012
Van Assche, Walter
1991
Polynomial interpolation and Gaussian quadrature for matrix-valued functions. Zbl 0810.41028
Sinap, Ann; Van Assche, Walter
1994
Nearest neighbor recurrence relations for multiple orthogonal polynomials. Zbl 1231.33014
Van Assche, Walter
2011
Relative asymptotics for orthogonal polynomials with a Sobolev inner product. Zbl 0771.42014
Marcellán, Francisco; Van Assche, Walter
1993
Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials. Zbl 1128.39013
Van Assche, Walter
2007
Orthogonal polynomials in the complex plane and on the real line. Zbl 0882.42013
Van Assche, Walter
1997
Orthogonal polynomials and Painlevé equations. Zbl 1387.33001
Van Assche, Walter
2018
Quadrature formulas based on rational interpolation. Zbl 0791.65011
Van Assche, Walter; Vanherwegen, Ingrid
1993
The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation. Zbl 1253.33012
Filipuk, Galina; Van Assche, Walter; Zhang, Lun
2012
Multiple orthogonal polynomials, irrationality and transcendence. Zbl 0952.42014
Van Assche, Walter
1999
Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight. Zbl 1061.30035
Aptekarev, A. I.; Van Assche, W.
2004
Upward extension of the Jacobi matrix for orthogonal polynomials. Zbl 0858.42015
Ronveaux, André; Van Assche, Walter
1996
The supports of measures associated with orthogonal polynomials and the spectra of the related self-adjoint operators. Zbl 0731.42021
Máté, Attila; Nevai, Paul; Van Assche, Walter
1991
Perturbation of orthogonal polynomials on an arc of the unit circle. Zbl 0842.42013
Golinskij, Leonid; Nevai, Paul; Van Assche, Walter
1995
Criterion for the resolvent set of nonsymmetric tridiagonal operators. Zbl 0824.47017
Aptekarev, A. I.; Kaliaguine, V.; Van Assche, Walter
1995
Asymptotics of Hermite-Padé rational approximants for two analytic functions with separated pairs of branch points (case of genus 0). Zbl 1156.41004
Aptekarev, Alexander I.; Kuijlaars, Arno B. J.; Van Assche, Walter
2008
Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials. Zbl 1187.39012
Boelen, Lies; van Assche, Walter
2010
Asymptotic properties of orthogonal polynomials from their recurrence formula. I. Zbl 0583.42011
Van Assche, Walter
1985
Multiple orthogonal polynomials associated with the modified Bessel functions of the first kind. Zbl 1025.33004
Coussement, Els; Van Assche, Walter
2003
Quadratic Hermite-Padé approximation to the exponential function: A Riemann-Hilbert approach. Zbl 1084.41007
Kuijlaars, A. B. J.; Assche, W.; Wielonsky, F.
2005
Lamé differential equations and electrostatics. Zbl 0952.34023
Dimitrov, Dimitar K.; Van Assche, Walter
2000
Approximating the weight function for orthogonal polynomials on several intervals. Zbl 0774.42015
Geronimo, J. S.; Van Assche, Walter
1991
Entropic integrals of hyperspherical harmonics and spatial entropy of $$D$$-dimensional central potentials. Zbl 0968.81011
Yáñez, R. J.; Van Assche, W.; González-Férez, R.; Dehesa, Jesús S.
1999
Asymptotic zero distribution for a class of multiple orthogonal polynomials. Zbl 1165.33007
Coussement, E.; Coussement, J.; van Assche, W.
2008
Information entropy of classical orthogonal polynomials and their application to the harmonic oscillator and Coulomb potentials. Zbl 0877.33005
Dehesa, Jesús S.; Van Assche, Walter; Yáñez, Rafael
1997
Asymptotics of multiple orthogonal polynomials associated with the modified Bessel functions of the first kind. Zbl 1078.33010
Coussement, Els; Van Assche, Walter
2003
Some properties of multiple orthogonal polynomials associated with Macdonald functions. Zbl 0984.33004
Coussement, Els; Van Assche, Walter
2001
Compact perturbations of orthogonal polynomials. Zbl 0723.42009
Nevai, Paul; Van Assche, Walter
1992
Sieved orthogonal polynomials and discrete measures with jumps dense in an interval. Zbl 0681.42016
Van Assche, Walter; Magnus, Alphonse P.
1989
Asymptotics for orthogonal polynomials with regularly varying recurrence coefficients. Zbl 0694.41039
Van Assche, Walter; Geronimo, Jeffrey S.
1989
Van Assche, Walter
2006
Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential. Zbl 0853.94011
Van Assche, Walter; Yáñez, R. J.; Dehesa, J. S.
1995
Extremal polynomials on discrete sets. Zbl 1033.42024
Kuijlaars, A. B. J.; Van Assche, W.
1999
Asymptotics for orthogonal polynomials and three-term recurrences. Zbl 0697.42023
Van Assche, Walter
1990
The impact of Stieltjes’ work on continued fractions and orthogonal polynomials: Additional material. Zbl 0856.33002
Valent, Galliano; Van Assche, Walter
1995
Recurrence coefficients of generalized Meixner polynomials and Painlevé equations. Zbl 1217.34135
Boelen, Lies; Filipuk, Galina; Van Assche, Walter
2011
Probabilistic proofs of asymptotic formulas for some classical polynomials. Zbl 0557.33006
Maejima, Makoto; Van Assche, Walter
1985
Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton $$q$$-Bessel function. Zbl 0855.33011
Koelink, H. T.; Van Assche, Walter
1995
Œuvres complètes. Collected papers. Ed. by Gerrit van Dijk. Volumes 1 and 2. Zbl 0779.01010
Stieltjes, Thomas Jan
1993
Little $$q$$-Legendre polynomials and irrationality of certain Lambert series. Zbl 1035.11032
Van Assche, Walter
2001
On the asymptotic distribution of eigenvalues of banded matrices. Zbl 0646.15004
Geronimo, Jeffrey S.; Harrell, Evans M. II; Van Assche, Walter
1988
Asymptotics for orthogonal polynomials on and off the essential spectrum. Zbl 0663.41029
Van Assche, Walter; Geronimo, Jeffrey S.
1988
The ratio of q-like orthogonal polynomials. Zbl 0634.33018
Van Assche, Walter
1987
Interlacing properties of zeros of multiple orthogonal polynomials. Zbl 1235.33007
Haneczok, Maciej; Van Assche, Walter
2012
Compact Jacobi matrices: From Stieltjes to Krein and $$M(a,b)$$. Zbl 0879.42013
Van Assche, Walter
1996
Analysis of non-linear recurrence relations for the recurrence coefficients of generalized Charlier polynomials. Zbl 1362.39018
van Assche, Walter; Foupouagnigni, Mama
2003
A random variable uniformly distributed between two independent random variables. Zbl 0641.60020
Van Assche, Walter
1987
Gaussian quadrature for multiple orthogonal polynomials. Zbl 1061.41021
Coussement, Jonathan; Van Assche, Walter
2005
Multiple Wilson and Jacobi–Piñeiro polynomials. Zbl 1066.33005
Beckermann, B.; Coussement, J.; Van Assche, W.
2005
Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice. Zbl 1018.37042
Aptekarev, A. I.; Van Assche, W.
2001
Differential equations for multiple orthogonal polynomials with respect to classical weights: raising and lowering operators. Zbl 1097.33004
Coussement, J.; van Assche, W.
2006
Hermite-Padé approximants for a pair of Cauchy transforms with overlapping symmetric supports. Zbl 1362.41001
Aptekarev, Alexander I.; van Assche, Walter; Yattselev, Maxim L.
2017
Information entropy of Gegenbauer polynomials. Zbl 1008.81015
Buyarov, V. S.; López-Artés, P.; Martínez-Finkelshtein, A.; Van Assche, W.
2000
Perturbation of orthogonal polynomials on an arc of the unit circle. II. Zbl 0958.42016
Golinskii, Leonid; Nevai, Paul; Pintér, Ferenc; van Assche, Walter
1999
Christoffel functions and Turán determinants on several intervals. Zbl 0790.42013
Van Assche, Walter
1993
Blumenthal’s theorem for Laurent orthogonal polynomials. Zbl 1022.42014
Sri Ranga, A.; Van Assche, Walter
2002
Asymptotic behavior of quadratic Hermite-Padé approximants to the exponential function and Riemann-Hilbert problems. (Asymptotique des approximants de Hermite-Padé quadratiques de la fonction exponentielle et problèmes de Riemann-Hilbert.) Zbl 1056.30038
Kuijlaars, Arno; Stahl, Herbert; Van Assche, Walter; Wielonsky, Franck
2003
Irrationality of $$\zeta _{q}(1)$$ and $$\zeta _{q}(2)$$. Zbl 1138.11027
Postelmans, Kelly; Van Assche, Walter
2007
Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials. Zbl 1001.35116
Coussement, J.; Kuijlaars, A. B. J.; Van Assche, W.
2002
Mehler-Heine asymptotics for multiple orthogonal polynomials. Zbl 1355.33014
van Assche, Walter
2017
Relative asymptotics for orthogonal polynomials with unbounded recurrence coefficients. Zbl 0705.42018
Geronimo, Jeffrey S.; Van Assche, Walter
1990
Para-orthogonal polynomials in frequency analysis. Zbl 1042.94001
Daruis, Leyla; Njåstad, Olav; Van Assche, Walter
2003
A family of nonlinear difference equations: existence, uniqueness, and asymptotic behavior of positive solutions. Zbl 1314.39017
Alsulami, Saud M.; Nevai, Paul; Szabados, József; Van Assche, Walter
2015
Discrete integrable systems generated by Hermite-Padé approximants. Zbl 1341.42043
Aptekarev, Alexander I.; Derevyagin, Maxim; van Assche, Walter
2016
Multiple orthogonal polynomials associated with an exponential cubic weight. Zbl 1309.42037
Van Assche, Walter; Filipuk, Galina; Zhang, Lun
2015
Type II Hermite-Padé approximation to the exponential function. Zbl 1119.41010
Kuijlaars, A. B. J.; Stahl, H.; Van Assche, W.; Wielonsky, F.
2007
Asymptotic properties of orthogonal polynomials from their recurrence formula. II. Zbl 0643.42019
Van Assche, Walter
1988
Recurrence coefficients of generalized Charlier polynomials and the fifth Painlevé equation. Zbl 1269.34095
Filipuk, Galina; Van Assche, Walter
2013
Riemann-Hilbert analysis for a Nikishin system. Zbl 1398.30024
López Lagomasino, G.; Van Assche, W.
2018
Functionals of Gegenbauer polynomials and $$D$$-dimensional hydrogenic momentum expectation values. Zbl 0977.33006
Van Assche, W.; Yáñez, R. J.; González-Férez, R.; Dehesa, Jesús S.
2000
Weak convergence of orthogonal polynomials. Zbl 0834.42013
Van Assche, Walter
1995
Orthogonal polynomials on a bi-lattice. Zbl 1262.34103
Smet, Christophe; Van Assche, Walter
2012
Computing recurrence coefficients of multiple orthogonal polynomials. Zbl 1328.65265
Filipuk, Galina; Haneczok, Maciej; Van Assche, Walter
2015
Products of 2$$\times 2$$ stochastic matrices with random entries. Zbl 0606.60012
Van Assche, Walter
1986
Multiple little $$q$$-Jacobi polynomials. Zbl 1068.33031
Postelmans, Kelly; Van Assche, Walter
2005
Recurrence coefficients of a new generalization of the Meixner polynomials. Zbl 1250.33015
Filipuk, Galina; Van Assche, Walter
2011
Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians. Zbl 1283.33010
Ndayiragije, F.; Van Assche, W.
2013
Asymptotics of entropy integrals for orthogonal polynomials. Zbl 0892.33005
Aptekarev, A. I.; Buyarov, V. S.; Van Assche, W.; Dehesa, J. S.
1996
Multidimensional Toda lattices: continuous and discrete time. Zbl 1341.42042
Aptekarev, Alexander I.; Derevyagin, Maxim; Miki, Hiroshi; Van Assche, Walter
2016
Spectral representation of four finite birth and death processes. Zbl 0971.60085
Van Assche, W.; Parthasarathy, P. R.; Lenin, R. B.
1999
Leonhard Euler and a $$q$$-analogue of the logarithm. Zbl 1188.33006
2009
WKB and turning point theory for second-order difference equations. Zbl 1064.39018
Geronimo, Jeffrey S.; Bruno, Oscar; van Assche, Walter
2004
Weighted zero distribution for polynomials orthogonal on an infinite interval. Zbl 0593.33010
Van Assche, Walter
1985
Unique positive solution for an alternative discrete Painlevé I equation. Zbl 1355.39005
Clarkson, Peter A.; Loureiro, Ana F.; van Assche, Walter
2016
On 2D discrete Schrödinger operators associated with multiple orthogonal polynomials. Zbl 1393.39012
Aptekarev, A. I.; Derevyagin, M.; van Assche, W.
2015
Three-fold symmetric Hahn-classical multiple orthogonal polynomials. Zbl 1435.33011
Loureiro, Ana F.; Van Assche, Walter
2020
Orthogonal and multiple orthogonal polynomials, random matrices, and Painlevé equations. Zbl 1443.33028
van Assche, Walter
2020
Encyclopedia of special functions: the Askey-Bateman project. Volume 1. Univariate orthogonal polynomials. With the assistance by Walter van Assche. Zbl 1466.33001
2020
Jacobi-Angelesco multiple orthogonal polynomials on an $$r$$-star. Zbl 1436.33008
Leurs, Marjolein; Van Assche, Walter
2020
Laguerre-Angelesco multiple orthogonal polynomials on an $$r$$-star. Zbl 1437.33008
Leurs, Marjolein; Van Assche, Walter
2020
Solution of an open problem about two families of orthogonal polynomials. Zbl 1412.42068
Van Assche, Walter
2019
Orthogonal polynomials and Painlevé equations. Zbl 1387.33001
Van Assche, Walter
2018
Riemann-Hilbert analysis for a Nikishin system. Zbl 1398.30024
López Lagomasino, G.; Van Assche, W.
2018
Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI. Zbl 1400.33016
Filipuk, Galina; Van Assche, Walter
2018
Hermite-Padé approximants for a pair of Cauchy transforms with overlapping symmetric supports. Zbl 1362.41001
Aptekarev, Alexander I.; van Assche, Walter; Yattselev, Maxim L.
2017
Mehler-Heine asymptotics for multiple orthogonal polynomials. Zbl 1355.33014
van Assche, Walter
2017
Alpert multiwavelets and Legendre-Angelesco multiple orthogonal polynomials. Zbl 1359.42016
Geronimo, Jeffrey S.; Iliev, Plamen; van Assche, Walter
2017
Discrete integrable systems generated by Hermite-Padé approximants. Zbl 1341.42043
Aptekarev, Alexander I.; Derevyagin, Maxim; van Assche, Walter
2016
Multidimensional Toda lattices: continuous and discrete time. Zbl 1341.42042
Aptekarev, Alexander I.; Derevyagin, Maxim; Miki, Hiroshi; Van Assche, Walter
2016
Unique positive solution for an alternative discrete Painlevé I equation. Zbl 1355.39005
Clarkson, Peter A.; Loureiro, Ana F.; van Assche, Walter
2016
What is $$\ldots$$ a multiple orthogonal polynomial? Zbl 1352.33002
Martínez-Finkelshtein, Andrei; Van Assche, Walter
2016
Asymptotic zero distribution of Jacobi-Piñeiro and multiple Laguerre polynomials. Zbl 1342.33024
Neuschel, Thorsten; Van Assche, Walter
2016
Ratio asymptotics for multiple orthogonal polynomials. Zbl 1355.42029
Van Assche, Walter
2016
Simultaneous Gaussian quadrature for Angelesco systems. Zbl 1377.41017
Lubinsky, Doron S.; Assche, Walter Van
2016
A family of nonlinear difference equations: existence, uniqueness, and asymptotic behavior of positive solutions. Zbl 1314.39017
Alsulami, Saud M.; Nevai, Paul; Szabados, József; Van Assche, Walter
2015
Multiple orthogonal polynomials associated with an exponential cubic weight. Zbl 1309.42037
Van Assche, Walter; Filipuk, Galina; Zhang, Lun
2015
Computing recurrence coefficients of multiple orthogonal polynomials. Zbl 1328.65265
Filipuk, Galina; Haneczok, Maciej; Van Assche, Walter
2015
On 2D discrete Schrödinger operators associated with multiple orthogonal polynomials. Zbl 1393.39012
Aptekarev, A. I.; Derevyagin, M.; van Assche, W.
2015
Hyperelliptic uniformization of algebraic curves of the third order. Zbl 1312.33022
Aptekarev, A. I.; Toulyakov, D. N.; Van Assche, W.
2015
Orthogonal polynomials for Minkowski’s question mark function. Zbl 1312.42031
Dresse, Zoé; Van Assche, Walter
2015
A tribute to Dick Askey. Zbl 1315.01039
2015
Variations of Stieltjes-Wigert and $$q$$-Laguerre polynomials and their recurrence coefficients. Zbl 1312.33059
Boelen, Lies; Van Assche, Walter
2015
Zero distribution of polynomials satisfying a differential-difference equation. Zbl 1303.33021
Dominici, Diego; van Assche, Walter
2014
Recurrence coefficients of generalized Charlier polynomials and the fifth Painlevé equation. Zbl 1269.34095
Filipuk, Galina; Van Assche, Walter
2013
Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians. Zbl 1283.33010
Ndayiragije, F.; Van Assche, W.
2013
The generalized Krawtchouk polynomials and the fifth Painlevé equation. Zbl 1279.33013
Boelen, Lies; Filipuk, Galina; Smet, Christophe; Van Assche, Walter; Zhang, Lun
2013
Ladder operators and differential equations for multiple orthogonal polynomials. Zbl 1271.33004
Filipuk, Galina; Van Assche, Walter; Zhang, Lun
2013
The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation. Zbl 1253.33012
Filipuk, Galina; Van Assche, Walter; Zhang, Lun
2012
Interlacing properties of zeros of multiple orthogonal polynomials. Zbl 1235.33007
Haneczok, Maciej; Van Assche, Walter
2012
Orthogonal polynomials on a bi-lattice. Zbl 1262.34103
Smet, Christophe; Van Assche, Walter
2012
Asymptotics for the ratio and the zeros of multiple Charlier polynomials. Zbl 1246.42022
Ndayiragije, François; Van Assche, Walter
2012
Nearest neighbor recurrence relations for multiple orthogonal polynomials. Zbl 1231.33014
Van Assche, Walter
2011
Recurrence coefficients of generalized Meixner polynomials and Painlevé equations. Zbl 1217.34135
Boelen, Lies; Filipuk, Galina; Van Assche, Walter
2011
Recurrence coefficients of a new generalization of the Meixner polynomials. Zbl 1250.33015
Filipuk, Galina; Van Assche, Walter
2011
Discrete Painlevé equations for recurrence coefficients of semiclassical Laguerre polynomials. Zbl 1187.39012
Boelen, Lies; van Assche, Walter
2010
Mellin transforms for multiple Jacobi-Piñeiro polynomials and a $$q$$-analogue. Zbl 1202.33007
Smet, Christophe; van Assche, Walter
2010
$$q$$-discrete Painlevé equations for recurrence coefficients of modified $$q$$-Freud orthogonal polynomials. Zbl 1189.39009
Boelen, Lies; Smet, Christophe; van Assche, Walter
2010
Orthogonal polynomials and approximation theory: some open problems. Zbl 1200.41014
Van Assche, Walter
2010
Special issue: Rolling waves in Leuven 2008. A international workshop on the occasion of Adhemar Bultheel’s 60th birthday. Selected papers based on the presentations at the workshop, Leuven, Belgium, December 15–16, 2008. Zbl 1205.65013
2010
Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Paperback reprint of the 2005 original. Zbl 1172.42008
2009
Leonhard Euler and a $$q$$-analogue of the logarithm. Zbl 1188.33006
2009
Irrationality proof of a $$q$$-extension of $$\zeta (2)$$ using little $$q$$-Jacobi polynomials. Zbl 1226.11074
Smet, Christophe; Van Assche, Walter
2009
Asymptotics of Hermite-Padé rational approximants for two analytic functions with separated pairs of branch points (case of genus 0). Zbl 1156.41004
Aptekarev, Alexander I.; Kuijlaars, Arno B. J.; Van Assche, Walter
2008
Asymptotic zero distribution for a class of multiple orthogonal polynomials. Zbl 1165.33007
Coussement, E.; Coussement, J.; van Assche, W.
2008
Varying weights for orthogonal polynomials with monotonically varying recurrence coefficients. Zbl 1143.42027
Aptekarev, A. I.; Geronimo, J. S.; Van Assche, W.
2008
Multiple orthogonal polynomials on the unit circle. Zbl 1172.41004
Ceniceros, Judit Minguez; Van Assche, Walter
2008
Discrete Painlevé equations for recurrence coefficients of orthogonal polynomials. Zbl 1128.39013
Van Assche, Walter
2007
Irrationality of $$\zeta _{q}(1)$$ and $$\zeta _{q}(2)$$. Zbl 1138.11027
Postelmans, Kelly; Van Assche, Walter
2007
Type II Hermite-Padé approximation to the exponential function. Zbl 1119.41010
Kuijlaars, A. B. J.; Stahl, H.; Van Assche, W.; Wielonsky, F.
2007
Rakhmanov’s theorem for orthogonal matrix polynomials on the unit circle. Zbl 1136.33005
Van Assche, Walter
2007
Difference equations, special functions and orthogonal polynomials. Proceedings of the international conference, Munich, Germany, July 25–30, 2005. Zbl 1117.39001
2007
Van Assche, Walter
2006
Differential equations for multiple orthogonal polynomials with respect to classical weights: raising and lowering operators. Zbl 1097.33004
Coussement, J.; van Assche, W.
2006
Orthogonal polynomials and special functions. Computation and applications. Lecture notes of the 5th European summer school, Madrid, Laganés, Spain, July 8–18, 2004. Zbl 1095.33001
2006
Classical and quantum orthogonal polynomials in one variable. With two chapters by Walter Van Assche. Zbl 1082.42016
2005
Quadratic Hermite-Padé approximation to the exponential function: A Riemann-Hilbert approach. Zbl 1084.41007
Kuijlaars, A. B. J.; Assche, W.; Wielonsky, F.
2005
Gaussian quadrature for multiple orthogonal polynomials. Zbl 1061.41021
Coussement, Jonathan; Van Assche, Walter
2005
Multiple Wilson and Jacobi–Piñeiro polynomials. Zbl 1066.33005
Beckermann, B.; Coussement, J.; Van Assche, W.
2005
Multiple little $$q$$-Jacobi polynomials. Zbl 1068.33031
Postelmans, Kelly; Van Assche, Walter
2005
A continuum limit of the relativistic Toda lattice: asymptotic theory of discrete Laurent orthogonal polynomials with varying recurrence coefficients. Zbl 1092.37049
Coussement, J.; van Assche, W.
2005
Szegő quadrature and frequency analysis. Zbl 1122.41017
Daruis, Leyla; Njåstad, Olav; Van Assche, Walter
2005
Generalizations of orthogonal polynomials. Zbl 1068.42021
Bultheel, A.; Cuyt, A.; Van Assche, W.; Van Barel, M.; Verdonk, B.
2005
The Riemann–Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]. Zbl 1082.42017
Kuijlaars, A. B. J.; Mclaughlin, K. T.-R.; Van Assche, W.; Vanlessen, M.
2004
Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight. Zbl 1061.30035
Aptekarev, A. I.; Van Assche, W.
2004
WKB and turning point theory for second-order difference equations. Zbl 1064.39018
Geronimo, Jeffrey S.; Bruno, Oscar; van Assche, Walter
2004
Difference equations for multiple Charlier and Meixner polynomials. Zbl 1068.33017
Van Assche, Walter
2004
An extension of the Toda lattice: a direct and inverse spectral transform connected with orthogonal rational functions. Zbl 1045.37041
Coussement, J.; Van Assche, W.
2004
Multiple orthogonal polynomials for classical weights. Zbl 1033.33002
Aptekarev, A. I.; Branquinho, A.; Van Assche, W.
2003
Some discrete multiple orthogonal polynomials. Zbl 1021.33006
Arvesú, J.; Coussement, J.; Van Assche, W.
2003
Multiple orthogonal polynomials associated with the modified Bessel functions of the first kind. Zbl 1025.33004
Coussement, Els; Van Assche, Walter
2003
Asymptotics of multiple orthogonal polynomials associated with the modified Bessel functions of the first kind. Zbl 1078.33010
Coussement, Els; Van Assche, Walter
2003
Analysis of non-linear recurrence relations for the recurrence coefficients of generalized Charlier polynomials. Zbl 1362.39018
van Assche, Walter; Foupouagnigni, Mama
2003
Asymptotic behavior of quadratic Hermite-Padé approximants to the exponential function and Riemann-Hilbert problems. (Asymptotique des approximants de Hermite-Padé quadratiques de la fonction exponentielle et problèmes de Riemann-Hilbert.) Zbl 1056.30038
Kuijlaars, Arno; Stahl, Herbert; Van Assche, Walter; Wielonsky, Franck
2003
Para-orthogonal polynomials in frequency analysis. Zbl 1042.94001
Daruis, Leyla; Njåstad, Olav; Van Assche, Walter
2003
Strong asymptotics for relativistic Hermite polynomials. Zbl 1035.33005
Gawronski, Wolfgang; Van Assche, Walter
2003
Blumenthal’s theorem for Laurent orthogonal polynomials. Zbl 1022.42014
Sri Ranga, A.; Van Assche, Walter
2002
Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials. Zbl 1001.35116
Coussement, J.; Kuijlaars, A. B. J.; Van Assche, W.
2002
Some classical multiple orthogonal polynomials. Zbl 0969.33005
Van Assche, Walter; Coussement, Els
2001
Riemann-Hilbert problems for multiple orthogonal polynomials. Zbl 0997.42012
Van Assche, Walter; Geronimo, Jeffrey S.; Kuijlaars, Arno B. J.
2001
Some properties of multiple orthogonal polynomials associated with Macdonald functions. Zbl 0984.33004
Coussement, Els; Van Assche, Walter
2001
Little $$q$$-Legendre polynomials and irrationality of certain Lambert series. Zbl 1035.11032
Van Assche, Walter
2001
Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice. Zbl 1018.37042
Aptekarev, A. I.; Van Assche, W.
2001
Ted Chihara and his work on orthogonal polynomials. Zbl 0999.01023
Askey, R.; Ismail, M. E. H.; Van Assche, W.
2001
Multiple orthogonal polynomials associated with Macdonald functions. Zbl 0959.42016
Van Assche, W.; Yakubovich, S. B.
2000
Lamé differential equations and electrostatics. Zbl 0952.34023
Dimitrov, Dimitar K.; Van Assche, Walter
2000
Information entropy of Gegenbauer polynomials. Zbl 1008.81015
Buyarov, V. S.; López-Artés, P.; Martínez-Finkelshtein, A.; Van Assche, W.
2000
Functionals of Gegenbauer polynomials and $$D$$-dimensional hydrogenic momentum expectation values. Zbl 0977.33006
Van Assche, W.; Yáñez, R. J.; González-Férez, R.; Dehesa, Jesús S.
2000
Nonsymmetric linear difference equations for multiple orthogonal polynomials. Zbl 0962.42016
Van Assche, Walter
2000
The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients. Zbl 0967.33009
Kuijlaars, A. B. J.; Van Assche, W.
1999
Multiple orthogonal polynomials, irrationality and transcendence. Zbl 0952.42014
Van Assche, Walter
1999
Entropic integrals of hyperspherical harmonics and spatial entropy of $$D$$-dimensional central potentials. Zbl 0968.81011
Yáñez, R. J.; Van Assche, W.; González-Férez, R.; Dehesa, Jesús S.
1999
Extremal polynomials on discrete sets. Zbl 1033.42024
Kuijlaars, A. B. J.; Van Assche, W.
1999
Perturbation of orthogonal polynomials on an arc of the unit circle. II. Zbl 0958.42016
Golinskii, Leonid; Nevai, Paul; Pintér, Ferenc; van Assche, Walter
1999
Spectral representation of four finite birth and death processes. Zbl 0971.60085
Van Assche, W.; Parthasarathy, P. R.; Lenin, R. B.
1999
Zero distribution of orthogonal polynomials with asymptotically periodic varying recurrence coefficients. Zbl 1002.42018
Van Assche, Walter
1999
...and 56 more Documents
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### Cited by 970 Authors

 86 Van Assche, Walter 63 Marcellán Español, Francisco 43 Kuijlaars, Arno B. J. 38 Aptekarev, Alexander Ivanovich 36 Martínez-Finkelshtein, Andrei 27 Dehesa, Jesús S. 20 Ranga, A. Sri 19 Durán, Antonio José 19 López Lagomasino, Guillermo Tomás 17 Branquinho, Amílcar José Pinto Lopes 17 Filipuk, Galina V. 16 Dette, Holger 16 Moreno-Balcázar, Juan José 16 Peherstorfer, Franz 15 Ismail, Mourad El-Houssieny 15 Zhang, Lun 14 Bultheel, Adhemar François 14 Xu, Shuaixia 14 Yattselev, Maxim L. 13 González-Vera, Pablo 13 Zhao, Yuqiu 12 Foulquié Moreno, Ana Pilar 12 Yáñez, Rafael J. 11 Bracciali, Cleonice Fátima 11 Geronimo, Jeffrey S. 11 Pijeira-Cabrera, Héctor 11 Suetin, Sergeĭ Pavlovich 10 Dominici, Diego Ernesto 10 Garza, Luis E. 10 Koelink, Erik 10 Lubinsky, Doron S. 10 Njåstad, Olav 10 Petronilho, José C. 9 Álvarez-Nodarse, Renato 9 Castillo, Kenier 9 Chen, Yang 9 Deaño, Alfredo 9 Derevyagin, Maxim S. 9 García-Ardila, Juan Carlos 9 Lysov, Vladimir G. 9 Nevai, Paul G. 9 Osilenker, Boris P. 9 Starovoĭtov, Aleksandr Pavlovich 9 Totik, Vilmos 9 Wong, Roderick Sue-Chuen 8 Charlier, Christophe 8 Dai, Dan 8 Delvaux, Steven 8 Golinskii, Leonid Borisovich 8 Magnus, Alphonse Ph. 8 Maroni, Pascal 8 Moral, Leandro 8 Rakhmanov, Evgenij Andreevich 8 Ronveaux, André 8 Sánchez-Moreno, Pablo 8 Shapiro, Boris Zalmanovich 8 Simon, Barry 8 Tulyakov, Dmitrii N. 8 Wielonsky, Franck 8 Zhedanov, Alexei S. 7 Alpan, Gökalp 7 Beckermann, Bernhard 7 Ben Cheikh, Youssèf 7 Cantero, María José 7 Clarkson, Peter A. 7 Duits, Maurice 7 Foupouagnigni, Mama 7 Grünbaum, Francisco Alberto 7 Huertas Cejudo, Edmundo José 7 Lamiri, Imed 7 Orive Rodríguez, Ramón Angel 7 Saff, Edward Barry 7 Smet, Christophe 7 Štampach, František 7 Yakubovich, Semyon B. 6 Barrios Rolanía, D. 6 Bleher, Pavel M. 6 Claeys, Tom 6 Gautschi, Walter 6 Griffin, James C. 6 Loureiro, Ana Filipa 6 Mañas, Manuel 6 Milovanović, Gradimir V. 6 Neuschel, Thorsten 6 Parthasarathy, Panamalai Ramarao 6 Piñar, Miguel A. 6 Rebocho, M. N. 6 Rezola, María Luisa 6 Román, Pablo Manuel 6 Silva, Guilherme L. F. 6 Stahl, Herbert Robert 6 Świderski, Grzegorz 6 Velázquez, Luis 5 Alfaro García, Manuel 5 Alhaidari, Abdulaziz D. 5 Arvesú, Jorge 5 Baratchart, Laurent 5 Ben Romdhane, Neila 5 Bonneux, Niels 5 Bourget, Alain ...and 870 more Authors
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### Cited in 210 Serials

 178 Journal of Approximation Theory 145 Journal of Computational and Applied Mathematics 50 Journal of Mathematical Analysis and Applications 39 Constructive Approximation 35 Linear Algebra and its Applications 31 Proceedings of the American Mathematical Society 30 Journal of Mathematical Physics 29 Communications in Mathematical Physics 29 Integral Transforms and Special Functions 25 Journal of Difference Equations and Applications 22 Applied Mathematics and Computation 21 Random Matrices: Theory and Applications 20 Numerical Algorithms 17 Mathematical Notes 17 Mathematics of Computation 17 Advances in Mathematics 16 Transactions of the American Mathematical Society 16 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 16 Proceedings of the Steklov Institute of Mathematics 14 Rocky Mountain Journal of Mathematics 14 Applied Numerical Mathematics 13 Journal d’Analyse Mathématique 9 Journal of Functional Analysis 9 Numerische Mathematik 9 Statistics & Probability Letters 9 Applied Mathematics Letters 9 Indagationes Mathematicae. New Series 9 Computational Methods and Function Theory 9 Analysis and Applications (Singapore) 7 Computers & Mathematics with Applications 7 Studies in Applied Mathematics 7 Sbornik: Mathematics 7 The Ramanujan Journal 7 Mediterranean Journal of Mathematics 6 Journal of Statistical Physics 6 Letters in Mathematical Physics 6 Theoretical and Mathematical Physics 6 Advances in Applied Mathematics 6 Acta Applicandae Mathematicae 6 Russian Journal of Mathematical Physics 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Complex Analysis and Operator Theory 5 Russian Mathematical Surveys 5 Duke Mathematical Journal 5 Transactions of the Moscow Mathematical Society 5 Analysis and Mathematical Physics 4 Communications on Pure and Applied Mathematics 4 Nonlinearity 4 Russian Mathematics 4 Advances in Computational Mathematics 4 Journal of Nonlinear Mathematical Physics 4 Journal of Physics A: Mathematical and Theoretical 4 Bulletin of Mathematical Sciences 3 Analysis Mathematica 3 Applicable Analysis 3 Nuclear Physics. B 3 International Journal of Mathematics and Mathematical Sciences 3 Journal of Differential Equations 3 Journal of Multivariate Analysis 3 Journal of Number Theory 3 Quaestiones Mathematicae 3 Acta Mathematica Hungarica 3 Journal of Theoretical Probability 3 SIAM Journal on Matrix Analysis and Applications 3 Journal of Scientific Computing 3 The Annals of Applied Probability 3 SIAM Journal on Mathematical Analysis 3 Journal of Mathematical Sciences (New York) 3 Journal of Mathematical Chemistry 3 Doklady Mathematics 3 Annales Henri Poincaré 3 Foundations of Computational Mathematics 3 Mathematics in Computer Science 3 Journal of Spectral Theory 3 Afrika Matematika 3 Problemy Fiziki, Matematiki i Tekhniki 2 International Journal of Theoretical Physics 2 Linear and Multilinear Algebra 2 Physica A 2 Physics Letters. A 2 Reports on Mathematical Physics 2 Ukrainian Mathematical Journal 2 Acta Mathematica 2 Annales de l’Institut Fourier 2 The Annals of Probability 2 BIT 2 Functional Analysis and its Applications 2 Integral Equations and Operator Theory 2 Journal of Applied Probability 2 Journal of Statistical Planning and Inference 2 Mathematische Nachrichten 2 Mathematica Slovaca 2 Memoirs of the American Mathematical Society 2 Monatshefte für Mathematik 2 Results in Mathematics 2 Zeitschrift für Analysis und ihre Anwendungen 2 Physica D 2 Journal of the American Mathematical Society 2 Queueing Systems 2 Experimental Mathematics ...and 110 more Serials
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### Cited in 53 Fields

 632 Special functions (33-XX) 533 Harmonic analysis on Euclidean spaces (42-XX) 224 Approximations and expansions (41-XX) 198 Functions of a complex variable (30-XX) 143 Linear and multilinear algebra; matrix theory (15-XX) 129 Probability theory and stochastic processes (60-XX) 117 Numerical analysis (65-XX) 112 Ordinary differential equations (34-XX) 108 Operator theory (47-XX) 83 Difference and functional equations (39-XX) 54 Quantum theory (81-XX) 48 Number theory (11-XX) 46 Dynamical systems and ergodic theory (37-XX) 42 Partial differential equations (35-XX) 41 Statistical mechanics, structure of matter (82-XX) 37 Statistics (62-XX) 35 Real functions (26-XX) 35 Information and communication theory, circuits (94-XX) 33 Potential theory (31-XX) 28 Integral transforms, operational calculus (44-XX) 25 Combinatorics (05-XX) 21 Sequences, series, summability (40-XX) 16 Functional analysis (46-XX) 9 History and biography (01-XX) 9 Computer science (68-XX) 7 Algebraic geometry (14-XX) 6 Measure and integration (28-XX) 6 Abstract harmonic analysis (43-XX) 5 Nonassociative rings and algebras (17-XX) 5 Topological groups, Lie groups (22-XX) 4 Integral equations (45-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Optics, electromagnetic theory (78-XX) 3 Group theory and generalizations (20-XX) 3 Geometry (51-XX) 3 Operations research, mathematical programming (90-XX) 3 Biology and other natural sciences (92-XX) 2 General and overarching topics; collections (00-XX) 2 Associative rings and algebras (16-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 2 Relativity and gravitational theory (83-XX) 2 Systems theory; control (93-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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