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Vorlesungen über Funktionentheorie: (110 Grundlehren der mathematischen Wissenschaften)

Vorlesungen über Funktionentheorie: (110 Grundlehren der mathematischen Wissenschaften)


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About the Book

Die vorliegende Einfiihrung in die Funktionentheorie ist aus Vor- lesungen entstanden, die ich vor 15 Jahren an der Friedrich-Wilhelms- Universitiit Berlin und spater, wenn man von einem einsemestrigeu Kur- sus liber Modem Theory of Functions an der Columbia University New York im Herbst 1952 absieht, wiederholt an der Freien Universitiit Berlin gehalten habe. Offen gesagt, hatte ich kaum die Zeit gefunden, diese Vorlesungen flir den Druck bereitzustelien, wenn uicht die Verzweiflung vieler meiner Harer, die manches Vorgetragene in der vorhandenen Literatur schwer finden konuten, mich zu dem EntschluB geflihrt hatte, auf Kosten anderer Arbeiten die Herausgabe dieses Buches zu beschleunigen. Was in diesen Vorlesungen geboten wird, ist nichts anderes als die Grundlage der Cauchy-Riemann-Nevanlinnaschen Funktionentheorie unter Zugrundelegung modemer Gesichtspunkte. Sie flihren den Leser bis an die Grenze eines groBen Teiles modemer Forschung und enthalten das, was meiner Meinung nach den Inhalt eines zwei-bzw. dreisemestri- gen Kursus liber Funktionentheorie an einer graBeren deutschen Uni- versitat ausmachen soli.

Table of Contents:
Erster Teil Die Grundlagen der Funktionentheorie.- Erstes Kapitel Die komplexe Ebene.- Zweites Kapitel Topologie der komplexen Ebene. Die Cauchysche Konvergenztheorie. Stetige Abbildungen.- Drittes Kapitel Lokale Eigenschaften der eindeutigen analytischen Funktionen.- Viertes Kapitel Die Hauptsätze der Cauchyschen Funktionentheorie.- Zweiter Teil Die Grundlagen der Riemann-Weierstraßschen Funktionentheorie.- Fünftes Kapitel Erzeugung analytischer Funktionen durch Grenzprozesse Der Riemann-Weierstraßsche Begriff der analytischen Funktion.- Sechstes Kapitel Die Eulersche Gammafunktion und die Riemannsche Zetafunktion.- Dritter Teil Maximumprinzip und Werteverteilung.- Siebentes Kapitel Majorisierungs- und Wachstumsprobleme.- Achtes Kapitel Geometrische Funktionentheorie. Konforme Abbildung.- Neuntes Kapitel Eindeutige analytische Funktionen in der Umgebung einer wesentlichen isolierten Singularität.- Namen- und Sachverzeichnis.


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Product Details
  • ISBN-13: 9783642948190
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 235 mm
  • No of Pages: 404
  • Returnable: N
  • Width: 155 mm
  • ISBN-10: 3642948197
  • Publisher Date: 18 Feb 2012
  • Binding: Paperback
  • Language: German
  • Returnable: N
  • Series Title: 110 Grundlehren der mathematischen Wissenschaften


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Vorlesungen über Funktionentheorie: (110 Grundlehren der mathematischen Wissenschaften)
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