Encyclopaedia of Mathematical Sciences Complex Analysis

Complex Analysis I

Entire and Meromorphic Functions Polyanalytic Functions and Their Generalizations

Editors: Gonchar, A.A., Havin, Viktor P., Nikolski, N.K. (Eds.)

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About this book

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.

Table of contents (2 chapters)

Table of contents (2 chapters)

Buy this book

eBook 96,29 €
price for Spain (gross)
  • ISBN 978-3-662-03396-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,79 €
price for Spain (gross)
  • ISBN 978-3-540-54703-7
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,79 €
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  • ISBN 978-3-642-08127-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Complex Analysis I
Book Subtitle
Entire and Meromorphic Functions Polyanalytic Functions and Their Generalizations
Editors
  • A.A. Gonchar
  • Viktor P. Havin
  • N.K. Nikolski
Translated by
Rublinetskij, V.I., Tkachenko, V.
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
85
Copyright
1997
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-03396-8
DOI
10.1007/978-3-662-03396-8
Hardcover ISBN
978-3-540-54703-7
Softcover ISBN
978-3-642-08127-9
Series ISSN
0938-0396
Edition Number
1
Number of Pages
IX, 261
Additional Information
Original Russian edition published by VINITI, Moscow, 1991
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