The Bergman Kernel and Related Topics
Author : Kengo Hirachi
Publisher : Springer Nature
Page : 372 pages
File Size : 49,41 MB
Release :
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ISBN : 981999506X
Author : Kengo Hirachi
Publisher : Springer Nature
Page : 372 pages
File Size : 49,41 MB
Release :
Category :
ISBN : 981999506X
Author : Takeo Ohsawa
Publisher :
Page : 186 pages
File Size : 12,88 MB
Release : 2006
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ISBN :
Author :
Publisher :
Page : 186 pages
File Size : 31,18 MB
Release : 2006
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Author : Xiaonan Ma
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 17,60 MB
Release : 2007-12-14
Category : Mathematics
ISBN : 3764381159
This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kähler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic torsion.
Author : Steven G. Krantz
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 46,71 MB
Release : 2013-09-20
Category : Mathematics
ISBN : 146147924X
This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.
Author : Stefan Bergman
Publisher : American Mathematical Soc.
Page : 269 pages
File Size : 44,97 MB
Release : 1950-03
Category : Mathematics
ISBN : 0821815059
The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of ""The Kernel Function"". The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable.
Author : Alexander A. Borichev
Publisher : American Mathematical Soc.
Page : 232 pages
File Size : 39,72 MB
Release : 2006
Category : Mathematics
ISBN : 0821837125
This volume grew out of a conference in honor of Boris Korenblum on the occasion of his 80th birthday, held in Barcelona, Spain, November 20-22, 2003. The book is of interest to researchers and graduate students working in the theory of spaces of analytic function, and, in particular, in the theory of Bergman spaces.
Author : Heinrich G W Begehr
Publisher : World Scientific
Page : 573 pages
File Size : 50,29 MB
Release : 2005-07-04
Category : Mathematics
ISBN : 981447990X
This authoritative volume comprises the plenary lectures and articles by many of the field's leading researchers who were brought together for the fourth time at the congress of the International Society for Analysis, its Applications and Computation (ISAAC).A wide spectrum of topics in modern analysis is covered by the fully refereed contributions, such as complex analysis, nonlinear analysis, inverse problems, wavelets, signals and images. In particular, important areas — not given special emphasis in previous meetings — include special functions and orthogonal polynomials, harmonic analysis, and partial differential equations.
Author : Guo Chun Wen
Publisher : World Scientific
Page : 338 pages
File Size : 15,4 MB
Release : 2000-02-22
Category : Science
ISBN : 981454311X
In this proceedings volume, the following topics are discussed: (1) various boundary value problems for partial differential equations and functional equations, including free and moving boundary problems; (2) the theory and methods of integral equations and integral operators, including singular integral equations; (3) applications of boundary value problems and integral equations to mechanics and physics; (4) numerical methods of integral equations and boundary value problems; and (5) some problems related with analysis and the foregoing subjects.
Author : John Ryan
Publisher : CRC Press
Page : 384 pages
File Size : 17,89 MB
Release : 2018-03-09
Category : Mathematics
ISBN : 1351460285
This new book contains the most up-to-date and focused description of the applications of Clifford algebras in analysis, particularly classical harmonic analysis. It is the first single volume devoted to applications of Clifford analysis to other aspects of analysis. All chapters are written by world authorities in the area. Of particular interest is the contribution of Professor Alan McIntosh. He gives a detailed account of the links between Clifford algebras, monogenic and harmonic functions and the correspondence between monogenic functions and holomorphic functions of several complex variables under Fourier transforms. He describes the correspondence between algebras of singular integrals on Lipschitz surfaces and functional calculi of Dirac operators on these surfaces. He also discusses links with boundary value problems over Lipschitz domains. Other specific topics include Hardy spaces and compensated compactness in Euclidean space; applications to acoustic scattering and Galerkin estimates; scattering theory for orthogonal wavelets; applications of the conformal group and Vahalen matrices; Newmann type problems for the Dirac operator; plus much, much more! Clifford Algebras in Analysis and Related Topics also contains the most comprehensive section on open problems available. The book presents the most detailed link between Clifford analysis and classical harmonic analysis. It is a refreshing break from the many expensive and lengthy volumes currently found on the subject.