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000800064 019__ $$a1004563624$$a1004904821
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000800064 020__ $$a3319632310$$q(electronic book)
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000800064 1001_ $$aKrantz, Steven G.$$q(Steven George),$$d1951-
000800064 24510 $$aHarmonic and complex analysis in several variables /$$cSteven G. Krantz.
000800064 260__ $$aCham :$$bSpringer,$$c2017.
000800064 300__ $$a1 online resource.
000800064 336__ $$atext$$btxt$$2rdacontent
000800064 337__ $$acomputer$$bc$$2rdamedia
000800064 338__ $$aonline resource$$bcr$$2rdacarrier
000800064 4901_ $$aSpringer monographs in mathematics
000800064 5050_ $$aPreface; Contents; 1 Introduction and Review; 1.1 Harmonic Analysis on the Disc; 1.1.1 The Boundary Behavior of Holomorphic Functions; Exercises; 2 Boundary Behavior; 2.1 The Modern Era; 2.1.1 Spaces of Homogeneous Type; 2.2 Estimates for the Poisson Kernel; 2.3 Subharmonicity and Boundary Values; 2.4 Pointwise Convergence for Harmonic Functions; 2.5 Boundary Values of Holomorphic Functions; 2.6 Admissible Convergence; Exercises; 3 The Heisenberg Group; 3.1 Prolegomena; 3.2 The Upper Half Plane in C; 3.3 The Significance of the Heisenberg Group; 3.4 The Heisenberg Group Action on U
000800064 5058_ $$a3.5 The Nature of ∂U3.6 The Heisenberg Group as a Lie Group; 3.7 Classical Analysis; 3.7.1 The Folland-Stein Theorem; 3.8 Calderón-Zygmund Theory; Exercises; 4 Analysis on the Heisenberg Group; 4.1 A Deeper Look at the Heisenberg Group; 4.2 L2 Boundedness of Calderón-Zygmund Integrals; 4.3 The Cotlar-Knapp-Stein Lemma; 4.4 Lp Boundedness of Calderón-Zygmund Integrals; 4.5 Calderón-Zygmund Applications; 4.6 The Szegő Integral on the Heisenberg Group; 4.7 The Poisson-Szegő Integral; 4.8 Applications of the Paley-Wiener Theorem; Exercises; 5 Reproducing Kernels; 5.1 Reproducing Kernels
000800064 5058_ $$a6.6 The Behavior of the Singularity6.7 A Real Bergman Space; 6.8 Relation Between Bergman and Szegő; 6.8.1 Introduction; 6.8.2 The Case of the Disc; 6.8.3 The Unit Ball in Cn; 6.8.4 Strongly Pseudoconvex Domains; 6.9 The Annulus; 6.10 Multiply Connected Domains; 6.11 The Sobolev Bergman Kernel; 6.12 The Theorem of Ramadanov; 6.13 More on the Szegő Kernel; 6.14 Boundary Localization; 6.14.1 Definitions and Notation; 6.14.2 A Representative Result; 6.14.3 The More General Result in the Plane; 6.14.4 Domains in Higher-Dimensional Complex Space; Exercises; 7 The Bergman Metric
000800064 5058_ $$a7.1 Smoothness of Biholomorphic Mappings7.2 The Bergman Metric at the Boundary; 7.3 Inequivalence of the Ball and the Polydisc; Exercises; 8 Geometric and Analytic Ideas; 8.1 Bergman Representative Coordinates; 8.2 The Berezin Transform; 8.2.1 Preliminary Remarks; 8.2.2 Introduction to the Poisson-Bergman Kernel; 8.2.3 Boundary Behavior; 8.3 Ideas of Fefferman; 8.4 The Invariant Laplacian; 8.5 The Dirichlet Problem for the Invariant Laplacian; 8.6 Concluding Remarks; Exercises; 9 Additional Analytic Topics; 9.1 The Worm Domain; 9.2 Additional Worm Ideas
000800064 506__ $$aAccess limited to authorized users.
000800064 520__ $$aAuthored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment; preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.
000800064 588__ $$aDescription based on print version record.
000800064 650_0 $$aHarmonic analysis.
000800064 77608 $$iPrint version:$$z9783319632292$$z3319632299$$w(OCoLC)992746993
000800064 830_0 $$aSpringer monographs in mathematics.
000800064 852__ $$bebk
000800064 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-63231-5$$zOnline Access$$91397441.1
000800064 909CO $$ooai:library.usi.edu:800064$$pGLOBAL_SET
000800064 980__ $$aEBOOK
000800064 980__ $$aBIB
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000800064 983__ $$aOnline
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