Complex analysis I
Subtitle: entire and meromorphic functions, polyanalytic functions and their generalizations
By: A.A. Gonchar, V.P. Havin, N.K. Nikolski (eds.).
Contributors: Gonchar, A. A.; Khavin, Viktor Petrovich.; Nikolʹskiĭ, N. K.
Series: Encyclopaedia of mathematical sciences -- v. 85.
Publisher: Springer
Published: 1997
Place of publication: Berlin; New York
Language: eng
Number of pages: 261
Subjects: Functions of complex variables; Functions, Entire; Functions, Meromorphic; Analytic functions; Fonctions entières; Fonctions méromorphes; Fonctions de plusieurs variables complexes
Work titles: Kompleksnyĭ analiz, odna peremennai͡a 1. English.
Description: 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. This contribution contains a detailed review of recent investigations concerning the function-theoretical peculiarities of polyanalytic functions (boundary behaviour, value distributions, degeneration, uniqueness etc.).
Notes: Includes bibliographical references and indexes.

Translated from the Russian.
Table of contents: title: Entire and meromorphic functions / A.A. Golʹdberg, B. Ya. Levin, I.V. Ostrovskii; title: Polyanalytic functions and their generalizations / M.B. Balk.