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Funktionentheorie I by K. Diederich, R. Remmert

Funktionentheorie I

by K. Diederich , R. Remmert
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Book cover type: Paperback
  • ISBN13: 9783540056829
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 248
  • Original Price: GBP 39.99
  • Language: German
  • Edition: N/A
  • Item Weight: 295 grams
  • BISAC Subject(s): Mathematical Analysis

Neue Blicke durch die alten Locher G. CH. liCHTENBERG o. Funktionentheorie ist nach klassischem Sprachgebrauch die Theorie der holomorphen Funktionen einer komplexen Veranderlichen. Der BegrifT der holomorphen Funktion kann im wesentlichen auf drei Weisen eingefUhrt werden: einmal durch die Forderung nach komplexer DifTerenzierbarkeit, zum anderen durch die Bedingung der Existenz einer Stammfunktion im Kleinen, und schlieBlich durch die Voraussetzung der lokalen Entwickelbar keit in eine Potenzreihe. Durch die Aquivalenz dieser methodisch verschiedenen Definitionen gewinnt die Funktionentheorie zu ihrem Reichtum die Ge schlossenheit hinzu, urn derentwillen C. L. Siegel sie in seinen Vorlesungen als ein einmaliges Geschenk an die Mathematiker bezeichnet. Dieses Taschenbuch ist der erste Teil einer zweibandigen Darstellung der Grundlagen der Funktionentheorie, die auf eine an der Universitat MUnster im Sommersemester 1968 und Wintersemester 1968/69 yom zweiten der beiden Autoren gehaltene Vorlesung zurUckgeht. Die beiden Zugange zur Funktionen theorie, die Cauchysche Theorie der komplex difTerenzierbaren Funktionen einschlieBlich der Theorie der Stammfunktionen und die WeierstraBsche Theorie der in Potenzreihen entwickelbaren Funktionen, werden darin zunachst unabhangig voneinander dargelegt. Dadurch wird insbesondere die Tragweite des WeierstraBschen Ansatzes deutlich, die in den heute meist gegebenen gemischten Darstellungen nicht so sichtbar wird. AuBerdem treten die StelJen im .Aufbau der Funktionentheorie besonders klar zu Tage, an denen das Zu sammenwirken der beiden Ansatze unumganglich zu sein scheint."

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