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The kernel function and conformal mapping
S Bergman

Mathematical Surveys and Monographs
1950; 257 pp; softcover
Volume: 5
ISBN-10: 0-8218-1505-9
ISBN-13: 978-0-8218-1505-2
List Price: US$57
Member Price: US$45.60
Order Code: SURV/5
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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.


Graduate students and research mathematicians interested in analysis.

Table of Contents

  • Orthogonal functions
  • The kernel function and associated minimum problems
  • The invariant metric and the method of the minimum integral
  • Kernel functions and Hilbert space
  • Representation of the classical domain functions
  • Canonical conformal transformations
  • Orthogonalization over the boundary
  • Variational methods
  • Existence proofs
  • Partial differential equations
  • Functions of two complex variables and pseudoconformal mapping
  • Generalization of potential-theoretical methods and certain subclasses of functions
  • Bibliography
  • Index
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