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Complex Analysis I

Entire and Meromorphic Functions Polyanalytic Functions and Their Generalizations

  • A. A. Gonchar
  • V. P. Havin
  • N. K. Nikolski

Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 85)

Table of contents

  1. Front Matter
    Pages i-ix
  2. A. A. Gol’dberg, B. Ya. Levin, I. V. Ostrovskii
    Pages 1-193
  3. Back Matter
    Pages 254-261

About this book

Introduction

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 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 book contains a detailed review of recent investigations concerning the function-theoretical pecularities of polyanalytic functions (boundary behavour, 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.

Keywords

Complex analysis Entire and meromorphic functionns Meromorphic function Nevanlinna theory Picardx type theorems boundary behaviour calculus ganze und meormorphe Funktionen generalized Cauchy-Riemann equations polyanalytic functions polynanlytisc

Editors and affiliations

  • A. A. Gonchar
    • 1
  • V. P. Havin
    • 2
    • 3
  • N. K. Nikolski
    • 4
  1. 1.Otdel MathematikiRussian Academy of SciencesMoscowRussia
  2. 2.Department of Mathematics and MechanicsSt. Petersburg State University, Stary PeterhofSt. PetersburgRussia
  3. 3.Department of Mathematics and StatisticsMcGill UniversityMontreal 1QCCanada
  4. 4.Départément de MathématiquesUniversité de Bordeaux ITalence, CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03396-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08127-9
  • Online ISBN 978-3-662-03396-8
  • Series Print ISSN 0938-0396
  • Buy this book on publisher's site