Overview

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

Full Product Details

Author:   Reinhold Remmert ,  L.D. Kay
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 1st ed. 1997
Volume:   172
Dimensions:   Width: 15.60cm , Height: 1.90cm , Length: 23.40cm
Weight:   0.575kg
ISBN:  

9781441931146

ISBN 10:   1441931147
Pages:   352
Publication Date:   01 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Infinite Products of Holomorphic Functions.- 2 The Gamma Function.- 3 Entire Functions with Prescribed Zeros.- 4* Holomorphic Functions with Prescribed Zeros.- 5 Iss’sa’s Theorem. Domains of Holomorphy.- 6 Functions with Prescribed Principal Parts.- 7 The Theorems of Montel and Vitali.- 8 The Riemann Mapping Theorem.- 9 Automorphisms and Finite Inner Maps.- 10 The Theorems of Bloch, Picard, and Schottky.- 11 Boundary Behavior of Power Series.- 12 Runge Theory for Compact Sets.- 13 Runge Theory for Regions.- 14 Invariance of the Number of Holes.- Short Biographies.- Symbol Index.- Name Index.

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