Mathematical Surveys and Monographs 1950; 257 pp; softcover Volume: 5 ISBN10: 0821815059 ISBN13: 9780821815052 List Price: US$57 Member Price: US$45.60 Order Code: SURV/5
 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 highspeed 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. Readership 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 potentialtheoretical methods and certain subclasses of functions
 Bibliography
 Index
