Classical Topics in Complex Function Theory: 172 (Graduate Texts in Mathematics, 172) - Tapa dura

Remmert, Reinhold

 
9780387982212: Classical Topics in Complex Function Theory: 172 (Graduate Texts in Mathematics, 172)
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ISBN 10: 0387982213 ISBN 13: 9780387982212
Editorial: Springer, 1997

Sinopsis

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

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De la contraportada

This book is an ideal text for an advanced course in the theory of complex functions. The author leads the reader to experience function theory personally and to participate in the work of the creative mathematician. The book contains numerous glimpses of the function theory of several complex variables, which illustrate how autonomous this discipline has become. Topics covered include Weierstrass's product theorem, Mittag-Leffler's theorem, the Riemann mapping theorem, and Runge's theorems on approximation of analytic functions. In addition to these standard topics, the reader will find Eisenstein's proof of Euler's product formula for the sine function; Wielandt's uniqueness theorem for the gamma function and applications; a detailed discussion of Stirling's formula; Iss'sa's theorem; Besse's proof that all domains in C are domains of holomorphy; Wedderburn's lemma and the ideal theory of rings of holomorphic functions; Estermann's proofs of the overconvergence theorem and Bloch's theorem; a holomorphic imbedding of the unit disc in C(superscript 3); and Gauss's expert opinion of November 1851 on Riemann's dissertation. Remmert 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, will make this book an invaluable source for students and teachers.

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Editorial
Springer
Año de publicación
1997
Idioma
Inglés
ISBN 10 
0387982213
ISBN 13 
9780387982212
Encuadernación
Tapa dura
Número de páginas
378
Contacto del fabricante
ROXIO
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Friedrich-Karl-Str. 9
Hamburg
22391
Alemania

Otras ediciones populares con el mismo título

9781441931146: Classical Topics in Complex Function Theory: 172 (Graduate Texts in Mathematics)

Edición Destacada

ISBN 10:  1441931147 ISBN 13:  9781441931146
Editorial: Springer, 2010
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