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Classical Topics in Complex Function Theory : Graduate Texts In Mathematics - R. Remmert

Classical Topics in Complex Function Theory

Graduate Texts In Mathematics

By: R. Remmert, L. D. Kay (Translator)

Hardcover

Published: 14th November 1997
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An ideal text for an advanced course in the theory of complex functions, this book leads readers to experience function theory personally and to participate in the work of the creative mathematician. The author includes numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. In addition to standard topics, readers will find Eisenstein's proof of Euler's product formula for the sine function; Wielandts uniqueness theorem for the gamma function; Stirlings formula; Isssas theorem; Besses proof that all domains in C are domains of holomorphy; Wedderburns lemma and the ideal theory of rings of holomorphic functions; Estermanns proofs of the overconvergence theorem and Blochs theorem; a holomorphic imbedding of the unit disc in C3; and Gausss expert opinion on Riemanns dissertation. Remmert elegantly presents the material in short clear sections, with compact proofs and historical comments interwoven throughout the text. The abundance of examples, exercises, and historical remarks, as well as the extensive bibliography, combine to make an invaluable source for students and teachers alike

Infinite Products and Partial Fraction Series
Infinite Poducts of Holomorphic Functions
The Gamma Function
Entire Functions with Prescribed Zeros
Holomorphic Functions with Prescribed Zeros
Iss'sa's Theorem. Regions of Holomorphy
Functions with Prescribed Principal Parts
Mapping Theory: The Theorems of Montel and Vitali
The Riemann Mapping Theorem
Appendix to Chapter 8 Caratheodory
Koebe Theory
Automorphisms and Finite Inner Maps
Selecta: The Theorems of Bloch, Picard, and Schottky
Boundary Behavior of Power Series
Runge Theory for Compact Sets
Runge Theory for Domains
Invariance of the Number of Holes
Short Biographies
Name
Index Subject
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387982212
ISBN-10: 0387982213
Series: Graduate Texts In Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 350
Published: 14th November 1997
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.77 x 16.51  x 2.54
Weight (kg): 0.7