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Functions of Completely Regular Growth : NATO Asi Series. Series C, Mathematical and Physical Science - L. I. Ronkin

Functions of Completely Regular Growth

NATO Asi Series. Series C, Mathematical and Physical Science

Hardcover

Published: 31st March 1992
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This monograph deals with functions of completely regular growth (FCRG), i.e., functions that have, in some sense, good asymptotic behaviour out of an exceptional set. The theory of entire functions of completely regular growth of on variable, developed in the late 1930s, soon found applications in both mathematics and physics. Later, the theory was extended to functions in the half-plane, subharmonic functions in space, and entire functions of several variables. This volume describes this theory and presents recent developments based on the concept of weak convergence. This enables a unified approach and provides a comparatively simple presentation of the classical Levin-Pfluger theory. Emphasis is put on those classes of functions which are particularly important for applications -- functions having a bounded spectrum and finite exponential sums.
For research mathematicians and physicists whose work involves complex analysis and its applications. The book will also be useful to those working in some areas of radiophysics and optics.

Series Editor's Preface
Preface
Entire functions of completely regular growth of one variablep. 1
Preliminariesp. 1
Regularity of growth, [actual symbols not reproducible]-convergence and right distribution of zerosp. 6
Rays of completely regular growth. Addition of indicatorsp. 29
Notesp. 40
Subharmonic functions of completely regular growth in [actual symbols not reproducible]p. 41
General information on subharmonic functions. [actual symbols not reproducible]-convergencep. 41
Criteria for regularity of growth in [actual symbols not reproducible]p. 69
Rays of completely regular growth and limit setsp. 84
Addition of indicatorsp. 94
Notesp. 99
Entire functions of completely regular growth in [actual symbols not reproducible]p. 101
Functions of c completely regular growth on complex raysp. 102
Addition of indicatorsp. 108
Entire functions with prescribed behaviour at infinityp. 112
Notesp. 140
Functions of completely regular growth in the half-plane or a conep. 141
Preliminary information on functions holomorphic in a half-planep. 141
Functions of completely regular growth in [actual symbols not reproducible]p. 172
Functions of completely regular growth in [actual symbols not reproducible]p. 189
Functions of completely regular growth in a conep. 221
Notesp. 242
Functions of exponential type and bounded on the real space (Fourier transforms of distribution of compact support)p. 244
Regularity of growth of entire functions of exponential type and bounded on the real spacep. 244
Discrete uniqueness setsp. 265
Norming setsp. 275
Notesp. 288
Quasipolynomialsp. 290
M-quasipolynomials. Growth and zero distributionp. 290
Entire functions that are quasipolynomials in every variablep. 300
Factors of quasipolynomialsp. 322
Notesp. 344
Mappingsp. 346
Information on the general theory of holomorphic mappingsp. 346
Plurisubharmonic functions of [alpha]-regular growth and asymptotic behaviour of order functions of holomorphic mappingsp. 360
Jessen's theorem for almost periodic holomorphic mappingsp. 368
Notesp. 379
Bibliographyp. 381
Subject Indexp. 391
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792316770
ISBN-10: 0792316770
Series: NATO Asi Series. Series C, Mathematical and Physical Science
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 392
Published: 31st March 1992
Publisher: SPRINGER VERLAG GMBH
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.39
Weight (kg): 0.74