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Fastperiodische Funktionen

Fastperiodische Funktionen

          
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About the Book

Das vorliegende Buch handelt von den fastperiodischen Funktionen auf Gruppen. Die Theorie dieser Funktionen erfaßt als Spezialfälle unter anderem die Fourierreihen periodischer Funktionen, die eigent- lichen von H. BOHR geschaffenen fastperiodischen Funktionen und die Kugelfunktionen. Im Grunde ist die Theorie der fastperiodischen Funk- tionen auf Gruppen nichts anderes als die Darstellungstheorie beliebiger, also vor allem auch unendlicher Gruppen. Als wichtigste Anwendung der Hauptsätze über fastperiodische Funktionen auf Gruppen darf man wohl die v. Neumannsehe Beweisführung ansehen, welche zeigt, daß jede kompakte, n-dimensionale Gruppe eine treue endliche unitäre Dar- stellung besitzt. Unter Benutzung von Sätzen aus v. Neumanns Theorie der linearen Gruppen kann hieraus gefolgert werden, daß jede kompakte n-dimensionale Gruppe eine Liesche kontinuierliche Gruppe ist. Das bekannte V. Hilbertsche Problem, welches sich allerdings auf noch allgemeinere, etwa lokalkompakte Gruppen bezieht, ist durch diesen Satz für den Fall kompakter Gruppen befriedigend gelöst. Alle an- gedeuteten Probleme, Sätze und Zusammenhänge werden in diesem Buche erläutert und bewiesen. Obwohl damit nur ein gewisser (wie mir scheint, besonders schöner) Ausschnitt aus dem Gesamtgebiet der Theorie fastperiodischer Funktionen wiedergegeben wird, dürfte der Leser wohl trotzdem durch die Lektüre in den Stand gesetzt werden, jede Abhandlung, welche sich auf fastperiodische Funktionen bezieht, ohne Schwierigkeiten zu verstehen. In dem letzten Abschnitt dieses Buches wird außerdem versucht, in kurzen Worten einen Überblick über das Gesamtgebiet der fastperiodischen Funktionen zu geben. Einzelne Literaturhinweise, die diesem Abschnitt beigefügt sind, wer- den möglicherweise alsdngenehm empfunden werden.


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Product Details
  • ISBN-13: 9783642866883
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 2
  • Language: German
  • Returnable: Y
  • Spine Width: 13 mm
  • Width: 156 mm
  • ISBN-10: 3642866883
  • Publisher Date: 06 May 2012
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 240
  • Series Title: Grundlehren Der Mathematischen Wissenschaften
  • Weight: 358 gr


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