Complex Analysis I: Entire and Meromorphic Functions, Polyanalytic Functions and Their Generalizations (Encyclopaedia of Mathematical Sciences, 8501) - Hardcover

Hardcover

ISBN 10: 0387547037 ISBN 13: 9780387547039

Synopsis

The first part of the volume contains a comprehensive description of the theory of entire and meromorphic functions of one complex variable and its applications. It includes the fundamental notions, methods and results on the growth of entire functions and the distribution of their zeros, the Rolf Nevanlinna theory of distribution of values of meromorphic functions including the inverse problem, the theory of completely regular growth, the concept of limit sets for entire and subharmonic functions. The authors describe the applications to the interpolation by entire functions, to entire and meromorphic solutions of ordinary differential equations, to the Riemann boundary problem with an infinite index and to the arithmetic of the convolution semigroup of probability distributions.
Polyanalytic functions form one of the most natural generalizations of analytic functions and are described in Part II. They emerged for the first time in plane elasticity theory where they found important applications (due to Kolossof, Mushelishvili etc.). This contribution contains a detailed review of recent investigations concerning the function-theoretical peculiarities of polyanalytic functions (boundary behaviour, value distributions, degeneration, uniqueness etc.). Polyanalytic functions have many points of contact with such fields of analysis as polyharmonic functions, Nevanlinna Theory, meromorphic curves, cluster set theory, functions of several complex variables etc.

Edition details

• ISBN 10: 0387547037
• ISBN 13: 9780387547039
• Binding: Hardcover
• Language: English
• Number of pages: 271