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## Krantz, Steven George

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 Author ID: krantz.steven-george Published as: Krantz, Steven G.; Krantz, S. G.; Krantz, Steven; Krantz, Steven George Homepage: https://www.math.wustl.edu/~sk/ External Links: MGP · Wikidata · ORCID · dblp · GND
 Documents Indexed: 297 Publications since 1976, including 82 Books Reviewing Activity: 195 Reviews
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#### Co-Authors

 153 single-authored 19 Greene, Robert Everist 19 Kim, Kang-Tae 13 Li, Songying 13 Peloso, Marco Maria 12 Parks, Harold R. 11 Isaev, Alexander 7 Ma, Daowei 4 Chang, Der-Chen E. 4 Fontana, Luigi 4 Fu, Siqi 3 Bedford, Eric 3 Blank, Brian E. 3 Chen, Goong 3 Cima, Joseph A. 3 Daghighi, Abtin 3 D’Angelo, John P. 3 Huang, Xiaojun 3 Rochberg, Richard 2 Alladi, Krishnaswami 2 Aron, Richard M. 2 Dao, Nguyen Anh 2 Douglas, Ronald George 2 Fridman, Buma L. 2 Gavosto, Estela Ana 2 Jorgenson, Jay Alan 2 Kahane, Jean-Pierre 2 Munao, Simone 2 Nathanson, Melvyn Bernard 2 Osserman, Robert 2 Parsons, Torrence D. 2 Sawyer, Eric T. 2 Stein, Elias Menachem 2 Stoppato, Caterina 2 Treil, Sergei 1 Agarwal, Ravi P. 1 Aladro, Gerardo 1 Alon, Noga M. 1 Bell, Steven R. 1 Bland, John S. 1 Bott, Raoul Harry 1 Burns, Daniel M. jun. 1 Byun, Jisoo 1 Casazza, Peter George 1 Chen, Zhenhua 1 Coleman, Matthew P. 1 Duncan, John 1 Earle, Clifford J. 1 Erdős, Pál 1 Fan, Dashan 1 Fornæss, John Erik 1 Garcia, Stephan Ramon 1 Gaussier, Hervé 1 Gehring, Frederick William 1 Godsil, Christopher David 1 Goldston, Daniel Alan 1 Graham, Ian R. 1 Graham, Ronald Lewis 1 Hejhal, Dennis A. 1 Hintikka, Eric A. 1 Jenkis, James 1 Jensen, Gary R. 1 Jewell, Nicholas P. 1 Jørgensen, Troels 1 Kaiser, Klaus Hermann 1 Kra, Irwin 1 Kuperberg, Gregory John 1 Lin, Peng 1 Liu, Bingyuan 1 Lovász, László 1 Marden, Albert 1 McCallum, William G. 1 McCarthy, John Edward 1 McNeal, Jeffery D. 1 Min, Baili 1 Pan, Yifei 1 Pang, Myungyull 1 Paulsen, William H. 1 Polyakov, Peter L. 1 Rădulescu, Vicenţiu D. 1 Rao, Arni S. R. Srinivasa 1 Royden, Halsey 1 Ruden, Randi D. 1 Russel, David L. 1 Salinas, Norberto 1 Sárközy, András 1 Sawyer, Stanley A. 1 Seo, Aeryeong 1 Shoemaker, Amy L. 1 Sós, Vera Turán 1 Spector, Daniel E. 1 Spencer, Joel H. 1 Spiro, Andrea F. 1 Stević, Stevo 1 Suffridge, Ted J. 1 Szabados, Jozsef 1 Tenenbaum, Gérald 1 van der Poorten, Alfred J. 1 Wayne, Clarence Eugene 1 Wegner, Bernd 1 West, Harry H. ...and 6 more Co-Authors
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#### Serials

 18 Complex Variables and Elliptic Equations 14 Journal of Mathematical Analysis and Applications 13 Textbooks in Mathematics 11 Rocky Mountain Journal of Mathematics 10 Notices of the American Mathematical Society 9 American Mathematical Monthly 7 Illinois Journal of Mathematics 7 Real Analysis Exchange 7 Complex Variables. Theory and Application 6 Michigan Mathematical Journal 5 Duke Mathematical Journal 5 Indiana University Mathematics Journal 5 Manuscripta Mathematica 5 The Journal of Geometric Analysis 4 Journal of the Korean Mathematical Society 4 Pacific Journal of Mathematics 4 Transactions of the American Mathematical Society 4 Expositiones Mathematicae 4 The Dolciani Mathematical Expositions 4 Complex Analysis and Operator Theory 3 Journal of Functional Analysis 3 Mathematische Annalen 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Proceedings of the American Mathematical Society 3 Bulletin of the Korean Mathematical Society 3 Mathematical Research Letters 3 The Carus Mathematical Monographs 3 Contemporary Mathematics 3 Proceedings of Symposia in Pure Mathematics 2 Houston Journal of Mathematics 2 Advances in Mathematics 2 International Journal of Mathematics and Mathematical Sciences 2 Journal of Differential Equations 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Zeitschrift 2 Bulletin of the American Mathematical Society. New Series 2 Graduate Studies in Mathematics 2 Cornerstones 1 Journal d’Analyse Mathématique 1 Studia Mathematica 1 Mathematics Magazine 1 The Mathematical Intelligencer 1 Annales de l’Institut Fourier 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin 1 Colloquium Mathematicum 1 Commentarii Mathematici Helvetici 1 Integral Equations and Operator Theory 1 Mathematica Scandinavica 1 Memoirs of the American Mathematical Society 1 Nagoya Mathematical Journal 1 Quaestiones Mathematicae 1 European Journal of Combinatorics 1 Journal of Symbolic Computation 1 Journal of the American Mathematical Society 1 Bulletin of the Allahabad Mathematical Society 1 Communications in Partial Differential Equations 1 SIAM Journal on Applied Mathematics 1 Experimental Mathematics 1 Electronic Research Announcements of the American Mathematical Society 1 The Journal of Fourier Analysis and Applications 1 The Asian Journal of Mathematics 1 Missouri Journal of Mathematical Sciences 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Bulletin of the American Mathematical Society 1 Fields Institute Communications 1 Graduate Texts in Mathematics 1 Lecture Notes in Mathematics 1 Mathematical Sciences Research Institute Publications 1 Progress in Mathematics 1 Regional Conference Series in Mathematics 1 Leituras em Matemática 1 Electronic Research Announcements in Mathematical Sciences 1 Synthesis Lectures on Mathematics and Statistics 1 Journal of Theoretical Biology 1 International Journal of Analysis and Applications 1 Modern Birkhäuser Classics 1 Applied and Numerical Harmonic Analysis 1 Springer Monographs in Mathematics 1 Birkhäuser Advanced Texts. Basler Lehrbücher 1 MAA Textbooks 1 Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs and Tracts 1 MAA Spectrum
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#### Fields

 166 Several complex variables and analytic spaces (32-XX) 47 Functions of a complex variable (30-XX) 38 General and overarching topics; collections (00-XX) 30 Partial differential equations (35-XX) 26 Real functions (26-XX) 24 Functional analysis (46-XX) 23 History and biography (01-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 14 Operator theory (47-XX) 11 Global analysis, analysis on manifolds (58-XX) 9 Potential theory (31-XX) 8 Mathematics education (97-XX) 6 Mathematical logic and foundations (03-XX) 6 Differential geometry (53-XX) 5 General topology (54-XX) 4 Ordinary differential equations (34-XX) 4 Abstract harmonic analysis (43-XX) 4 Integral equations (45-XX) 4 Convex and discrete geometry (52-XX) 4 Computer science (68-XX) 3 Measure and integration (28-XX) 3 Geometry (51-XX) 3 Manifolds and cell complexes (57-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Algebraic geometry (14-XX) 2 Topological groups, Lie groups (22-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of deformable solids (74-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Field theory and polynomials (12-XX) 1 Group theory and generalizations (20-XX) 1 Difference and functional equations (39-XX) 1 Sequences, series, summability (40-XX) 1 Integral transforms, operational calculus (44-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Algebraic topology (55-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Mechanics of particles and systems (70-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

196 Publications have been cited 2,527 times in 1,889 Documents Cited by Year
Function theory of several complex variables. Zbl 0471.32008
Krantz, Steven G.
1982
Function theory of several complex variables. Reprint of the 1992 2nd ed. with corrections. Zbl 1087.32001
Krantz, Steven G.
2001
A primer of real analytic functions. 2nd ed. Zbl 1015.26030
Krantz, Steven G.; Parks, Harold R.
2002
Function theory of several complex variables. 2. ed. Zbl 0776.32001
Krantz, Steven G.
1992
The implicit function theorem. History, theory, and applications. Zbl 1012.58003
Krantz, Steven G.; Parks, Harold R.
2002
Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary. Zbl 0807.32008
Burns, Daniel M.; Krantz, Steven G.
1994
A primer of real analytic functions. Zbl 0767.26001
Krantz, Steven; Parks, Harold R.
1992
$$H^ p$$ theory on a smooth domain in $$\mathbb{R}^ N$$ and elliptic boundary value problems. Zbl 0804.35027
Chang, Der-Chen; Krantz, Steven G.; Stein, Elias M.
1993
Deformation of complex structures, estimates for the (partial d) equation, and stability of the Bergman kernel. Zbl 0504.32016
Greene, Robert E.; Krantz, Steven G.
1982
On the iterated logarithmic Bloch space on the unit ball. Zbl 1221.47056
Krantz, Steven G.; Stević, Stevo
2009
Geometric integration theory. Zbl 1149.28001
Krantz, Steven G.; Parks, Harold R.
2008
Distance to $$C^k$$ hypersurfaces. Zbl 0431.57009
Krantz, Steven G.; Parks, Harold R.
1981
Domains with non-compact automorphism group: a survey. Zbl 1040.32019
Isaev, A. V.; Krantz, S. G.
1999
The geometry of domains in space. Zbl 0929.26001
Krantz, Steven G.; Parks, Harold R.
1999
Boundedness and compactness of integral operators on spaces of homogeneous type and applications. I. Zbl 0990.47042
Krantz, Steven G.; Li, Song-Ying
2001
Lipschitz spaces, smoothness of functions, and approximation theory. Zbl 0518.46018
Krantz, Steven G.
1983
Optimal Lipschitz and $$L^p$$ regularity for the equation $$\overline\partial u=f$$ on strongly pseudo-convex domains. Zbl 0303.35059
Krantz, S. G.
1976
Geometric function theory. Explorations in complex analysis. Zbl 1086.30001
Krantz, Steven G.
2006
Boundedness and compactness of integral operators on spaces of homogeneous type and applications. II. Zbl 0990.47043
Krantz, Steven G.; Li, Song-Ying
2001
Handbook of complex variables. Zbl 0946.30001
Krantz, Steven G.
1999
The Schwarz lemma at the boundary. Zbl 1227.30023
Krantz, Steven G.
2011
The Lindelöf principle and normal functions of several complex variables. Zbl 0522.32003
Cima, Joseph A.; Krantz, Steven G.
1983
The automorphism groups of strongly pseudoconvex domains. Zbl 0531.32016
Greene, Robert E.; Krantz, Steven G.
1982
Function theory of one complex variable. 3rd ed. Zbl 1114.30001
Greene, Robert E.; Krantz, Steven G.
2006
The Bergman kernel and projection on non-smooth worm domains. Zbl 1161.32016
Krantz, Steven G.; Peloso, Marco M.
2008
A criterion for normality in $$\mathbb{C}^ n$$. Zbl 0749.32001
1991
On the automorphism groups of hyperbolic manifolds. Zbl 0974.32018
Isaev, Alexander V.; Krantz, Steven G.
2001
Duality theorems for Hardy and Bergman spaces on convex domains of finite type in $${\mathbb{C}}^ n$$. Zbl 0835.32004
Krantz, Steven G.; Li, Song-Ying
1995
The implicit function theorem. History, theory, and applications. Reprint of the 2003 hardback edition. Zbl 1269.58003
Krantz, Steven G.; Parks, Harold R.
2013
On a problem of Moser. Zbl 0846.32010
Huang, Xiaojun; Krantz, Steven G.
1995
Bloch functions on strongly pseudoconvex domains. Zbl 0628.32006
Krantz, Steven G.; Ma, Daowei
1988
The geometry of complex domains. Zbl 1239.32011
Greene, Robert E.; Kim, Kang-Tae; Krantz, Steven G.
2011
Analysis, designs, and behaviour of dissipative joints for coupled beams. Zbl 0685.73046
Chen, G.; Krantz, S. G.; Russel, D. L.; Wayne, C. E.; West, H. H.; Coleman, M. P.
1989
Compactness of the $$\bar \partial$$-Neumann operator. Zbl 0736.35071
Krantz, Steven G.
1988
Complex scaling and domains with non-compact automorphism group. Zbl 1065.32014
Kim, Kang-Tae; Krantz, Steven G.
2001
Techniques for studying automorphisms of weakly pseudoconvex domains. Zbl 0779.32017
Greene, Robert E.; Krantz, Steven G.
1993
On decomposition theorems for Hardy spaces on domains in $$\mathbb{C}^ n$$ and applications. Zbl 0886.32003
Krantz, Steven G.; Li, Song-Ying
1995
Smoothness to the boundary of conformal maps. Zbl 0626.30005
Bell, Steven R.; Krantz, Steven G.
1987
Hardy spaces and elliptic boundary value problems. Zbl 0765.42014
Chang, Der-Chen; Krantz, Steven G.; Stein, Elias M.
1992
A panorama of harmonic analysis. Zbl 0947.42001
Krantz, Steven G.
1999
A note on the Wong-Rosay theorem in complex manifolds. Zbl 1044.32019
Gaussier, Hervé; Kim, Kang-Tae; Krantz, Steven G.
2002
Invariant metrics and the boundary behavior of holomorphic functions on domains in $${\mathbb{C}}^ n$$. Zbl 0728.32002
Krantz, Steven G.
1991
Fractional integration on Hardy spaces. Zbl 0504.47034
Krantz, Steven G.
1982
Analysis and geometry on worm domains. Zbl 1147.32020
Krantz, Steven G.; Peloso, Marco M.
2008
Invariants of Bergman geometry and the automorphism groups of domains in $${\mathbb{C}^n}$$. Zbl 0997.32012
Greene, R. E.; Krantz, S. G.
1991
Characterization of complex manifolds by the isotropy subgroups of their automorphism groups. Zbl 0622.32020
Greene, Robert E.; Krantz, Steven G.
1985
Geometric Lipschitz spaces and applications to complex function theory and nilpotent groups. Zbl 0428.41004
Krantz, Steven G.
1979
Intrinsic Lipschitz classes on manifolds with applications to complex function theory and estimates for the $$\overline\partial$$ and $$\overline\partial_b$$ equations. Zbl 0382.32012
Krantz, Steven G.
1978
Geometric analysis of the Bergman kernel and metric. Zbl 1281.32004
Krantz, Steven G.
2013
Explorations in harmonic analysis. With applications to complex function theory and the Heisenberg group. Zbl 1171.43001
Krantz, Steven G.
2009
Holomorphic functions of bounded mean oscillation and mapping properties of the Szegö projection. Zbl 0456.32004
Krantz, Steven G.
1980
A unique continuation problem for holomorphic mappings. Zbl 0781.32018
Huang, Xiaojun; Krantz, Steven G.
1993
Biholomorphic self-maps of domains. Zbl 0625.32024
Greene, Robert E.; Krantz, Steven G.
1987
The boundary behavior of the Kobayashi metric. Zbl 0760.32010
Krantz, Steven G.
1992
A note on Hardy spaces and functions of bounded mean oscillation on domains in $$\mathbb{C}^ n$$. Zbl 0802.32013
Krantz, Steven G.; Li, Song-Ying
1994
Partial differential equations and complex analysis. Zbl 0852.35001
Krantz, Steven George; Gavosto, Estela A.; Peloso, Marco M.
1992
Normal families and the semicontinuity of isometry and automorphism groups. Zbl 0584.58014
Greene, Robert E.; Krantz, Steven G.
1985
Complex analysis: the geometric viewpoint. Zbl 0743.30002
Krantz, Steven G.
1990
Stability properties of the Bergman kernel and curvature properties of bounded domains. Zbl 0483.32014
Greene, R. E.; Krantz, Steven G.
1981
Geometric analysis and function spaces. Expository lectures from the NSF- CBMS regional conference held at George Mason University, Fairfax, VA (USA), May 26-31, 1992. Zbl 0783.32001
Krantz, Steven G.
1993
Optimal $$L^ p$$ estimates for the $$\bar \partial$$-equation on complex ellipsoids in $$\mathbb{C}^ n$$. Zbl 0789.32011
Chen, Zhenhua; Krantz, Steven G.; Ma, Daowei
1993
On the Bergman invariant and curvatures of the Bergman metric. Zbl 0855.32008
Krantz, Steven G.; Yu, Jiye
1996
Stability of the Caratheodory and Kobayashi metrics and applications to biholomorphic mappings. Zbl 0533.32011
Greene, Robert E.; Krantz, Steven G.
1984
Area integral characterizations of functions in Hardy spaces on domains in $$\mathbb{C}^ n$$. Zbl 0887.32002
Krantz, Steven G.; Li, Song-Ying
1997
On fixed points and determining sets for holomorphic automorphisms. Zbl 1026.32042
Fridman, B. L.; Kim, K. T.; Krantz, S. G.; Ma, D.
2002
A Hopf lemma for holomorphic functions and applications. Zbl 0837.30019
Huang, Xiaojun; Krantz, S. G.; Ma, D.; Pan, Y.
1995
Reinhardt domains with non-compact automorphism groups. Zbl 0866.32001
Fu, Siqi; Isaev, A. V.; Krantz, Steven G.
1996
Calculation and estimation of the Poisson kernel. Zbl 1060.31004
Krantz, Steven G.
2005
The Kobayashi metric of a complex ellipsoid in $$\mathbb{C}^ 2$$. Zbl 0783.32012
Blank, Brian E.; Fan, Dashan; Klein, David; Krantz, Steven G.; Ma, Daowei; Pang, Myung-Yull
1992
Structure and interpolation theorems for certain Lipschitz spaces and estimates for the $$\overline\partial$$ equation. Zbl 0357.46037
Krantz, Steven G.
1976
Complex scaling and geometric analysis of several variables. Zbl 1156.32001
Kim, Kang-Tae; Krantz, Steven G.
2008
Analysis on the Heisenberg group and estimates for functions in Hardy classes of several complex variables. Zbl 0401.43004
Krantz, Steven G.
1979
Complex analysis: the geometric viewpoint. 2nd ed. Zbl 1051.30001
Krantz, Steven G.
2004
Characterization of the Hilbert ball by its automorphism group. Zbl 1007.32002
Kim, Kang-Tae; Krantz, Steven G.
2002
Bergman kernel and projection on the unbounded Diederich-Fornaess worm domain. Zbl 1377.32003
Krantz, Steven G.; Peloso, Marco M.; Stoppato, Caterina
2016
On the vector sum of two convex sets in space. Zbl 0728.52003
Krantz, Steven G.; Parks, Harold R.
1991
A guide to complex variables. Zbl 1147.30001
Krantz, Steven G.
2008
On the boundary orbit accumulation set for a domain with noncompact automorphism group. Zbl 0879.32016
Isaev, A. V.; Krantz, S. G.
1996
Lipschitz spaces on stratified groups. Zbl 0529.22006
Krantz, Steven
1982
Some new results on domains in complex space with non-compact automorphism group. Zbl 1035.32019
Kim, Kang-Tae; Krantz, Steven G.
2003
Characterizations of certain weakly pseudoconvex domains with non-compact automorphism groups. Zbl 0626.32023
Greene, Robert E.; Krantz, Steven G.
1987
Antisocial subcovers of self-centered coverings. Zbl 0631.52013
Krantz, Steven G.; Parsons, T. D.
1986
Asymptotic eigenfrequency distributions for the $$N$$-beam Euler-Bernoulli coupled beam equation with dissipative joints. Zbl 0746.35025
Krantz, Steven G.; Paulsen, William H.
1991
Boundary values and estimates for holomorphic functions of several complex variables. Zbl 0431.32004
Krantz, Steven G.
1980
Toeplitz operators and related function algebras on certain pseudo-convex domains. Zbl 0371.47029
Jewell, Nicholas P.; Krantz, Steven G.
1979
On the dimensions of the automorphism groups of hyperbolic Reinhardt domains. Zbl 0968.32001
Gifford, J. A.; Isaev, A. V.; Krantz, S. G.
2000
Geometric characterizations of centroids of simplices. Zbl 1089.52009
Krantz, Steven G.; McCarthy, John E.; Parks, Harold R.
2006
A reflection principle for proper holomorphic mappings of strongly pseudoconvex domains and applications. Zbl 0518.32009
Cima, Joseph A.; Krantz, Steven G.; Suffridge, Ted J.
1984
Characterization of smooth domains in C by their biholomorphic self-maps. Zbl 0524.30007
Krantz, Steven G.
1983
A matter of gravity. Zbl 1045.51007
Krantz, Steven G.
2003
Fatou theorems on domains in $${\mathbb{C}}^ n$$. Zbl 0614.32007
Krantz, Steven G.
1987
The Kobayashi metric, extremal discs, and biholomorphic mappings. Zbl 1246.32012
Krantz, Steven G.
2012
A Kobayashi metric version of Bun Wong’s theorem. Zbl 1172.32002
Kim, Kang-Tae; Krantz, Steven G.
2009
On isometric isomorphisms of the Bloch space on the unit ball of $${\mathbb{C}}^ n$$. Zbl 0687.32022
Krantz, Steven G.; Ma, Daowei
1989
A characterization of generalized complex ellipsoids in $$\mathbb{C}^ n$$ and related results. Zbl 0782.32027
Krantz, Steven G.
1992
Convexity in complex analysis. Zbl 0739.32019
Krantz, Steven G.
1991
A direct connection between the Bergman and Szegő projections. Zbl 1297.32005
Krantz, Steven G.
2014
New results on the Bergman kernel of the worm domain in complex space. Zbl 1140.32310
Krantz, Steven G.; Peloso, Marco M.
2008
Nonlinear conditions for differentiability of functions. Zbl 0632.58008
Duncan, John; Krantz, Steven G.; Parks, Harold R.
1985
Intersection graphs for families of balls in $$R^n$$. Zbl 0659.05079
Erdős, Paul; Godsil, C. D.; Krantz, S. G.; Parsons, T. D.
1988
$$L^p$$ regularity of the Bergman projection on domains covered by the polydisc. Zbl 1457.32003
Chen, Liwei; Krantz, Steven G.; Yuan, Yuan
2020
The Besicovitch covering lemma and maximal functions. Zbl 1418.42030
Krantz, Steven G.
2019
Canonical kernels versus constructible kernels. Zbl 1429.30016
Krantz, Steven G.
2019
Geometric analysis on the Diederich-Fornæss index. Zbl 1400.32018
Krantz, Steven George; Liu, Bingyuan; Peloso, Marco Maria
2018
On a theorem of F. Forelli and a result of Hartogs. Zbl 1387.32003
Krantz, Steven G.
2018
Uniqueness properties of Hardy space functions. Zbl 1393.32003
Krantz, Steven G.
2018
The weighted Bergman kernel and the Green’s function. Zbl 1361.30096
Krantz, Steven; Wójcicki, Paweł M.
2017
Harmonic and complex analysis in several variables. Zbl 1414.32001
Krantz, Steven G.
2017
A primer of mathematical writing. Being a disquisition on having your ideas recorded, typeset, published, read, and appreciated. 2nd edition. Zbl 1390.00064
Krantz, Steven G.
2017
Bergman kernel and projection on the unbounded Diederich-Fornaess worm domain. Zbl 1377.32003
Krantz, Steven G.; Peloso, Marco M.; Stoppato, Caterina
2016
The Greene-Krantz conjecture in dimension two. Zbl 1405.32026
Krantz, Steven G.
2016
Local maximum modulus property for polyanalytic functions. Zbl 1332.30070
Daghighi, Abtin; Krantz, Steven G.
2016
Erratum: A note on a conjecture concerning boundary uniqueness. Zbl 1403.30014
Daghighi, Abtin; Krantz, Steven
2016
Convex analysis. Zbl 1310.26001
Krantz, Steven G.
2015
Reflections on Paul Erdős on his birth centenary. Zbl 1338.01020
Alladi, Krishnaswami; Krantz, Steven; Lóvasz, László; Sós, Vera T.; Graham, Ronald L.; Spencer, Joel; Kahane, Jean-Pierre; Nathanson, Melvyn B.
2015
Smoothness to the boundary of biholomoprhic mappings: an overview. Zbl 1345.32016
Krantz, Steven G.
2015
A note on a conjecture concerning boundary uniqueness. Zbl 1319.30027
Daghighi, Abtin; Krantz, Steven G.
2015
A direct connection between the Bergman and Szegő projections. Zbl 1297.32005
Krantz, Steven G.
2014
The Corona problem in several complex variables. Zbl 1317.32004
Krantz, Steven G.
2014
The impact of the theorem of Bun Wong and Rosay. Zbl 1290.32019
Krantz, Steven G.
2014
The Corona problem. Connections between operator theory, function theory, and geometry. Selected papers based on the workshop, Toronto, Canada, June 2012. Zbl 1297.30004
Douglas, Ronald G.; Krantz, Steven G.; Sawyer, Eric T.; Treil, Sergei; Wick, Brett D.
2014
Real analysis and foundations. 3rd ed. Zbl 1278.26001
Krantz, Steven G.
2014
The implicit function theorem. History, theory, and applications. Reprint of the 2003 hardback edition. Zbl 1269.58003
Krantz, Steven G.; Parks, Harold R.
2013
Geometric analysis of the Bergman kernel and metric. Zbl 1281.32004
Krantz, Steven G.
2013
The Carathéodory and Kobayashi/Royden metrics by way of dual extremal problems. Zbl 1277.32014
Royden, Halsey; Wong, Pit-Mann; Krantz, Steven G.
2013
The automorphism groups of domains in complex space: a survey. Zbl 1274.32001
Krantz, Steven G.
2013
Semicontinuity of automorphism groups of strongly pseudoconvex domains: the low differentiability case. Zbl 1271.32021
Greene, Robert E.; Kim, Kang-Tae; Krantz, Steven G.; Seo, Aeryeong
2013
On limits of sequences of holomorphic functions. Zbl 1294.30011
Krantz, Steven G.
2013
The Kobayashi metric, extremal discs, and biholomorphic mappings. Zbl 1246.32012
Krantz, Steven G.
2012
The automorphism group of a domain with an exponentially flat boundary point. Zbl 1227.32031
Krantz, Steven G.
2012
Geometric properties of boundary orbit accumulation points. Zbl 1247.32020
Krantz, Steven G.
2012
The Schwarz lemma at the boundary. Zbl 1227.30023
Krantz, Steven G.
2011
The geometry of complex domains. Zbl 1239.32011
Greene, Robert E.; Kim, Kang-Tae; Krantz, Steven G.
2011
Convergence of automorphisms and semicontinuity of automorphism groups. Zbl 1271.32018
Krantz, Steven G.
2011
The proof is in the pudding. The changing nature of mathematical proof. Zbl 1318.00005
Krantz, Steven G.
2011
Convexity in real analysis. Zbl 1246.26010
Krantz, Steven G.
2011
Boundary decomposition of the Bergman kernel. Zbl 1226.30006
Krantz, Steven G.
2011
On a construction of L. Hua for positive reproducing kernels. Zbl 1197.32002
Krantz, Steven G.
2010
Essentials of topology with applications. Zbl 1178.54001
Krantz, Steven G.
2010
The corona problem with two pieces of data. Zbl 1204.32004
Krantz, Steven G.
2010
Normed domains of holomorphy. Zbl 1196.32009
Krantz, Steven G.
2010
On the iterated logarithmic Bloch space on the unit ball. Zbl 1221.47056
Krantz, Steven G.; Stević, Stevo
2009
Explorations in harmonic analysis. With applications to complex function theory and the Heisenberg group. Zbl 1171.43001
Krantz, Steven G.
2009
A Kobayashi metric version of Bun Wong’s theorem. Zbl 1172.32002
Kim, Kang-Tae; Krantz, Steven G.
2009
A guide to topology. Zbl 1170.54001
Krantz, Steven G.
2009
An ontology of directional regularity implying joint regularity. Zbl 1186.26008
Krantz, Steven G.
2009
Geometric integration theory. Zbl 1149.28001
Krantz, Steven G.; Parks, Harold R.
2008
The Bergman kernel and projection on non-smooth worm domains. Zbl 1161.32016
Krantz, Steven G.; Peloso, Marco M.
2008
Analysis and geometry on worm domains. Zbl 1147.32020
Krantz, Steven G.; Peloso, Marco M.
2008
Complex scaling and geometric analysis of several variables. Zbl 1156.32001
Kim, Kang-Tae; Krantz, Steven G.
2008
A guide to complex variables. Zbl 1147.30001
Krantz, Steven G.
2008
New results on the Bergman kernel of the worm domain in complex space. Zbl 1140.32310
Krantz, Steven G.; Peloso, Marco M.
2008
The Carathéodory and Kobayashi metrics and applications in complex analyis. Zbl 1177.30060
Krantz, Steven G.
2008
A tale of three kernels. Zbl 1157.32005
Krantz, Steven G.
2008
Pseudoconvexity, analytic discs and invariant metrics. Zbl 1162.32007
Krantz, Steven G.
2008
The Hartogs extension phenomenon redux. Zbl 1140.32007
Krantz, Steven G.
2008
The Carathéodory-Cartan-Kaup-Wu theorem on an infinite-dimensional Hilbert space. Zbl 1143.46024
Cima, Joseph A.; Graham, Ian; Kim, Kang Tae; Krantz, Steven G.
2007
The Lindelöf principle in several complex variables. Zbl 1109.32006
Krantz, Steven G.
2007
On functions in $$p$$-adic $$BMO$$ and the distribution of prime integers. Zbl 1119.46029
Krantz, Steven G.
2007
A tribute to Professor william f. ames on his 80th birthday. Zbl 1151.01322
Agarwal, Ravi P.; Krantz, Steven G.
2007
The boundary behavior of holomorphic functions: global and local results. Zbl 1141.32002
Krantz, Steven G.
2007
How to write your first paper. Zbl 1145.00301
Krantz, Steven G.
2007
Geometric function theory. Explorations in complex analysis. Zbl 1086.30001
Krantz, Steven G.
2006
Function theory of one complex variable. 3rd ed. Zbl 1114.30001
Greene, Robert E.; Krantz, Steven G.
2006
Geometric characterizations of centroids of simplices. Zbl 1089.52009
Krantz, Steven G.; McCarthy, John E.; Parks, Harold R.
2006
On determining sets for holomorphic automorphisms. Zbl 1144.32012
Fridman, B. L.; Kim, K.-T.; Krantz, S. G.; Ma, D.
2006
Calculation and estimation of the Poisson kernel. Zbl 1060.31004
Krantz, Steven G.
2005
Analytic polyhedra in $$\mathbb C^2$$ with a non-compact automorphism group. Zbl 1062.32020
Kim, Kang-Tae; Krantz, Steven G.; Spiro, Andrea F.
2005
Real analysis and foundations. 2nd ed. Zbl 1056.26001
Krantz, Steven G.
2005
The automorphism groups of domains. Zbl 1138.32302
Kim, Kang-Tae; Krantz, Steven G.
2005
Mathematical apocrypha redux. More stories and anecdotes of mathematicians and the mathematical. Zbl 1082.00002
Krantz, Steven G.
2005
Two results on uniqueness of conformal mappings. Zbl 1083.30010
Krantz, Steven G.
2005
Mathematical publishing. A guidebook. Zbl 1084.00004
Krantz, Steven G.
2005
Complex analysis: the geometric viewpoint. 2nd ed. Zbl 1051.30001
Krantz, Steven G.
2004
Creating more convergent series. Zbl 1044.40001
Krantz, Steven G.; McNeal, Jeffery D.
2004
Some new results on domains in complex space with non-compact automorphism group. Zbl 1035.32019
Kim, Kang-Tae; Krantz, Steven G.
2003
A matter of gravity. Zbl 1045.51007
Krantz, Steven G.
2003
Normal families of holomorphic functions and mappings on a Banach space. Zbl 1069.46026
Kim, Kang-Tae; Krantz, Steven G.
2003
The Bergman metric invariants and their boundary behavior. Zbl 1048.32002
Kim, Kang-Tae; Krantz, Steven G.
2003
Determining sets and fixed points for holomorphic endomorphisms. Zbl 1053.32010
Kim, Kang-Tae; Krantz, Steven G.
2003
A primer of real analytic functions. 2nd ed. Zbl 1015.26030
Krantz, Steven G.; Parks, Harold R.
2002
The implicit function theorem. History, theory, and applications. Zbl 1012.58003
Krantz, Steven G.; Parks, Harold R.
2002
A note on the Wong-Rosay theorem in complex manifolds. Zbl 1044.32019
Gaussier, Hervé; Kim, Kang-Tae; Krantz, Steven G.
2002
On fixed points and determining sets for holomorphic automorphisms. Zbl 1026.32042
Fridman, B. L.; Kim, K. T.; Krantz, S. G.; Ma, D.
2002
Characterization of the Hilbert ball by its automorphism group. Zbl 1007.32002
Kim, Kang-Tae; Krantz, Steven G.
2002
Function theory of one complex variable. 2nd ed. Zbl 0988.30001
Greene, Robert E.; Krantz, Steven G.
2002
Determination of a domain in complex space by its automorphism group. Zbl 1030.32018
Krantz, Steven G.
2002
A smoothly bounded domain in a complex surface with a compact quotient. Zbl 1028.32010
Cheung, Wing Sum; Fu, Siqi; Krantz, Steven G.; Wong, Bun
2002
Function theory of several complex variables. Reprint of the 1992 2nd ed. with corrections. Zbl 1087.32001
Krantz, Steven G.
2001
Boundedness and compactness of integral operators on spaces of homogeneous type and applications. I. Zbl 0990.47042
Krantz, Steven G.; Li, Song-Ying
2001
Boundedness and compactness of integral operators on spaces of homogeneous type and applications. II. Zbl 0990.47043
Krantz, Steven G.; Li, Song-Ying
2001
On the automorphism groups of hyperbolic manifolds. Zbl 0974.32018
Isaev, Alexander V.; Krantz, Steven G.
2001
Complex scaling and domains with non-compact automorphism group. Zbl 1065.32014
Kim, Kang-Tae; Krantz, Steven G.
2001
Dictionary of algebra, arithmetic, and trigonometry. Zbl 0967.00001
Krantz, Steven G.
2001
On the dimensions of the automorphism groups of hyperbolic Reinhardt domains. Zbl 0968.32001
Gifford, J. A.; Isaev, A. V.; Krantz, S. G.
2000
Fatou theorems old and new: An overview of the boundary behavior of holomorphic functions. Zbl 0965.32007
Krantz, Steven G.
2000
Characterization of Reinhardt domains by their automorphism groups. Zbl 0965.32005
Isaev, Alexander V.; Krantz, Steven G.
2000
Invariant distances and metrics in complex analysis. Zbl 1040.32012
Isaev, Alexander V.; Krantz, Steven G.
2000
Domains with non-compact automorphism group: a survey. Zbl 1040.32019
Isaev, A. V.; Krantz, S. G.
1999
The geometry of domains in space. Zbl 0929.26001
Krantz, Steven G.; Parks, Harold R.
1999
...and 96 more Documents
all top 5

#### Cited by 2,191 Authors

 84 Krantz, Steven George 26 Kim, Kang-Tae 22 Stević, Stevo 15 Liu, Taishun 14 Yang, Dachun 13 Tu, Zhenhan 12 Chang, Der-Chen E. 12 Isaev, Alexander 12 Li, Songying 12 Shoikhet, David 11 de la Llave, Rafael 11 Huang, Xiaojun 10 Byun, Jisoo 10 Ninh Văn Thu 10 Örnek, Bülent Nafi 10 Peloso, Marco Maria 10 Tang, Xiaomin 9 Duong, Xuan Thinh 9 Fridman, Buma L. 9 Gaussier, Hervé 9 Lee, Kang-Hyurk 9 Ma, Daowei 9 Verma, Kaushal 8 Chen, Shaolin 8 Ha, Ly Kim 8 McNeal, Jeffery D. 8 Yang, Sibei 8 Zeytuncu, Yunus Ergýn 8 Zimmer, Andrew M. 7 Brackx, Fred F. 7 Choe, Boo Rim 7 De Schepper, Hennie 7 Fornæss, John Erik 7 Greene, Robert Everist 7 Liu, Bingyuan 7 Peralta-Salas, Daniel 7 Seshadri, Harish 7 Straube, Emil J. 7 Yamamori, Atsushi 7 Yan, Lixin 7 Yang, Dongyong 6 Bernal-Gonzàlez, Luis 6 Boas, Harold P. 6 Bracci, Filippo 6 Čučković, Željko 6 Fu, Siqi 6 Guo, Kunyu 6 Lanzani, Loredana 6 Lebl, Jiří 6 Li, Songxiao 6 Mitrea, Marius 6 Nestoridis, Vassili 6 Noell, Alan V. 6 Pan, Yifei 6 Şahutoğlu, Sönmez 6 Shamoyan, Romi F. 6 Stein, Elias Menachem 6 Wang, Jianfei 6 Zhang, Liyou 5 Agler, Jim 5 Alpay, Daniel Aron 5 Cao, Jun 5 Chakrabarti, Debraj 5 Chen, Bo-Yong 5 Cho, Hong Rae 5 Ding, Yong 5 Elin, Mark 5 Engliš, Miroslav 5 Gong, Sheng 5 Harrington, Phillip S. 5 Haslinger, Friedrich 5 Kim, Hyeseon 5 Klep, Igor 5 Lee, Young Joo 5 Liu, Yongmin 5 Monguzzi, Alessandro 5 Nicolay, Samuel 5 Nikolov, Nikolai Marinov 5 Popescu, Gelu 5 Ren, Guangbin 5 Shapiro, Michael V. 5 Sommen, Franciscus 5 Ungar, Abraham Albert 5 Wick, Brett D. 5 Wu, Huoxiong 5 Yin, Wanke 5 Yu, Yanyan 5 Zheng, Dechao 5 Zhou, Xiangyu 4 Barrett, David E. 4 Berhanu, Shiferaw 4 Bolotnikov, Vladimir 4 Bonet Solves, José 4 Bortolussi, Luca 4 Bory Reyes, Juan 4 Cao, Guangfu 4 Capogna, Luca 4 Caraballo, David G. 4 Cho, Sanghyun 4 Choi, Young-Jun ...and 2,091 more Authors
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#### Cited in 403 Serials

 151 Journal of Mathematical Analysis and Applications 104 The Journal of Geometric Analysis 71 Proceedings of the American Mathematical Society 59 Transactions of the American Mathematical Society 53 Journal of Functional Analysis 46 Mathematische Annalen 45 Complex Variables and Elliptic Equations 44 Advances in Mathematics 32 Mathematische Zeitschrift 29 Applied Mathematics and Computation 28 Complex Analysis and Operator Theory 24 Journal of Differential Equations 21 Duke Mathematical Journal 21 Integral Equations and Operator Theory 19 Journal d’Analyse Mathématique 18 Annales de l’Institut Fourier 18 Science China. Mathematics 17 Rocky Mountain Journal of Mathematics 15 Michigan Mathematical Journal 15 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 14 Annali di Matematica Pura ed Applicata. Serie Quarta 14 Linear Algebra and its Applications 14 Journal of Inequalities and Applications 13 Manuscripta Mathematica 13 Science in China. Series A 12 Communications in Mathematical Physics 12 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 12 Journal of Approximation Theory 12 International Journal of Mathematics 12 Comptes Rendus. Mathématique. Académie des Sciences, Paris 11 Archiv der Mathematik 11 Monatshefte für Mathematik 11 Communications in Partial Differential Equations 11 Bulletin of the American Mathematical Society. New Series 10 Inventiones Mathematicae 10 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 10 Computational Methods and Function Theory 9 Israel Journal of Mathematics 9 Results in Mathematics 9 Potential Analysis 9 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 9 Acta Mathematica Sinica. English Series 8 Mathematische Nachrichten 8 Tohoku Mathematical Journal. Second Series 8 Calculus of Variations and Partial Differential Equations 8 Bulletin des Sciences Mathématiques 8 The Journal of Fourier Analysis and Applications 8 Journal of Function Spaces 7 Archive for Rational Mechanics and Analysis 7 Computers & Mathematics with Applications 7 Mathematical Notes 7 Automatica 7 Nagoya Mathematical Journal 7 Systems & Control Letters 7 Annals of Global Analysis and Geometry 7 Revista Matemática Iberoamericana 7 SIAM Journal on Mathematical Analysis 7 Indagationes Mathematicae. New Series 7 Analysis and Mathematical Physics 6 Bulletin of the Australian Mathematical Society 6 Journal of Statistical Physics 6 Mathematical Methods in the Applied Sciences 6 Collectanea Mathematica 6 Journal of Computational and Applied Mathematics 6 Journal of the American Mathematical Society 6 Geometric and Functional Analysis. GAFA 6 Journal de Mathématiques Pures et Appliquées. Neuvième Série 6 Journal of Mathematical Sciences (New York) 6 Advances in Applied Clifford Algebras 6 Abstract and Applied Analysis 6 Complex Analysis and its Synergies 5 Arkiv för Matematik 5 Chaos, Solitons and Fractals 5 Kodai Mathematical Journal 5 Memoirs of the American Mathematical Society 5 Pacific Journal of Mathematics 5 Chinese Annals of Mathematics. Series B 5 Constructive Approximation 5 Expositiones Mathematicae 5 Annales Academiae Scientiarum Fennicae. Mathematica 5 Communications of the Korean Mathematical Society 5 Mediterranean Journal of Mathematics 4 Applicable Analysis 4 Journal of Mathematical Physics 4 Annales Polonici Mathematici 4 Czechoslovak Mathematical Journal 4 Illinois Journal of Mathematics 4 Journal of Economic Theory 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Topology and its Applications 4 Physica D 4 Probability Theory and Related Fields 4 Journal of Complexity 4 Information and Computation 4 Journal of Global Optimization 4 Stochastic Processes and their Applications 4 Mathematical Programming. Series A. Series B 4 Advances in Geometry 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 4 Asian-European Journal of Mathematics ...and 303 more Serials
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#### Cited in 60 Fields

 814 Several complex variables and analytic spaces (32-XX) 285 Operator theory (47-XX) 281 Functions of a complex variable (30-XX) 257 Partial differential equations (35-XX) 224 Functional analysis (46-XX) 163 Harmonic analysis on Euclidean spaces (42-XX) 120 Differential geometry (53-XX) 85 Global analysis, analysis on manifolds (58-XX) 74 Dynamical systems and ergodic theory (37-XX) 70 Numerical analysis (65-XX) 68 Potential theory (31-XX) 65 Real functions (26-XX) 63 Probability theory and stochastic processes (60-XX) 62 Ordinary differential equations (34-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 47 Systems theory; control (93-XX) 39 Approximations and expansions (41-XX) 36 Convex and discrete geometry (52-XX) 33 Linear and multilinear algebra; matrix theory (15-XX) 32 Mechanics of deformable solids (74-XX) 31 Fluid mechanics (76-XX) 30 Algebraic geometry (14-XX) 30 Operations research, mathematical programming (90-XX) 29 Statistics (62-XX) 29 Quantum theory (81-XX) 27 Combinatorics (05-XX) 25 Measure and integration (28-XX) 25 Statistical mechanics, structure of matter (82-XX) 23 Topological groups, Lie groups (22-XX) 21 Abstract harmonic analysis (43-XX) 20 Computer science (68-XX) 19 Number theory (11-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 17 Mathematical logic and foundations (03-XX) 17 Manifolds and cell complexes (57-XX) 16 Special functions (33-XX) 16 Difference and functional equations (39-XX) 16 Integral equations (45-XX) 16 Geometry (51-XX) 16 General topology (54-XX) 16 Biology and other natural sciences (92-XX) 15 Mechanics of particles and systems (70-XX) 12 Group theory and generalizations (20-XX) 11 Information and communication theory, circuits (94-XX) 9 History and biography (01-XX) 9 Relativity and gravitational theory (83-XX) 7 Integral transforms, operational calculus (44-XX) 6 Field theory and polynomials (12-XX) 3 General and overarching topics; collections (00-XX) 3 Associative rings and algebras (16-XX) 3 Optics, electromagnetic theory (78-XX) 3 Geophysics (86-XX) 3 Mathematics education (97-XX) 2 Commutative algebra (13-XX) 2 Nonassociative rings and algebras (17-XX) 2 Category theory; homological algebra (18-XX) 2 Sequences, series, summability (40-XX) 1 $$K$$-theory (19-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Astronomy and astrophysics (85-XX)

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