Articoli correlati a Classical Topics in Complex Function Theory: 172
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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
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Contenuti
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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Book by Remmert Reinhold
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 the. Codice articolo 5913208
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Buch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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; 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 C3; and Gauss's expert opinion of November 1851 on Riemann's 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, will make this book an invaluable source for students and teachers. 376 pp. Englisch. Codice articolo 9780387982212
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Classical Topics in Complex Function Theory (Graduate Texts in Mathematics, 172)
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Buch. Condizione: Neu. Neuware -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 alikeSpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 376 pp. Englisch. Codice articolo 9780387982212
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Buch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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; 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 C3; and Gauss's expert opinion of November 1851 on Riemann's 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, will make this book an invaluable source for students and teachers. Codice articolo 9780387982212
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