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Lineare Integraloperatoren by Konrad Jörgens

Lineare Integraloperatoren

by Konrad Jörgens
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Book cover type: Paperback
  • ISBN13: 9783519022053
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 224
  • Original Price: EUR 42.05
  • Language: German
  • Edition: 1970
  • Item Weight: 368 grams
  • BISAC Subject(s): Engineering (General)

Die Rand- und Eigenwertprobleme der Mathematischen Physik lassen sich fast alle in Integralgleichungen umformen. Der Aufbau der Theorie der Integralgleichungen durch 1. Fredholm, D. Hilbert und E. Schmidt zu Beginn unseres Jahrhunderts brachte daher gro e Fortschritte f�r die Mathematische Physik. Obwohl sp�ter andere und zum Teil weit- reichendere Methoden gefunden worden sind, ist die Integralgleichungsmethode noch heute ein wirkungsvolles und vor allem in der Physik und den Ingenieurwissenschaften viel benutztes Instrument zur Behandlung solcher Probleme. Mit den Integralgleichungen begann die Entwicklung der heutigen Funktionalanalysis, deren Hauptgegenstand die Untersuchung der linearen Operatoren von einem topologischen Vektorraum in einen anderen ist. Die Theorie der Integralgleichungen erscheint in diesem Rahmen als Spezialfall: Die betrachteten Vektorr�ume sind hier Banachsche Funktionen- r�ume, die Operatoren Integraloperatoren. Das Eigenwertproblem f�r eine Integralgleichung erweist sich als Spezialfall der Spektraltheorie linearer Operatoren. Die Verwendung der Begriffe und Methoden der Funktionalanalysis macht die Theorie der Integralgleichungen nicht nur einheitlicher und durchsichtiger, sie vereinfacht und erweitert sie so wesentlich, da eine moderne Darstellung ohne diese Elemente nicht denkbar ist. Andererseits gen�gt es nicht, die Theorie der Integralgleichungen als Nebenprodukt oder Beispielsammlung im Rahmen der Funktionalanalysis abzuhandeln; eine solche Auffassung wird den Erforder- nissen der Anwendungen nicht gerecht. Im vorliegenden Buch wird daher ein mittlerer Weg eingeschlagen: Es wird eine Einf�hrung in die Funktionalanalysis vorausgeschickt, die in Umfang und Stoff auswahl auf die Integraloperatoren zugeschnitten ist; darauffolgt eine Theorie der Integraloperatoren mit ausf�hrlicher Darstellung der typischen Anwendungen.

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