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Lineare Integraloperatoren

Lineare Integraloperatoren


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About the Book

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 große Fortschritte für die Mathematische Physik. Obwohl später 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 Vektorräume sind hier Banachsche Funktionen- räume, die Operatoren Integraloperatoren. Das Eigenwertproblem für 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, daß eine moderne Darstellung ohne diese Elemente nicht denkbar ist. Andererseits genügt 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 Einführung in die Funktionalanalysis vorausgeschickt, die in Umfang und Stoff auswahl auf die Integraloperatoren zugeschnitten ist; darauf folgt eine Theorie der Integraloperatoren mit ausführlicher Darstellung der typischen Anwendungen.


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Product Details
  • ISBN-13: 9783519022053
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Height: 244 mm
  • No of Pages: 224
  • Series Title: Mathematische Leitfäden
  • Weight: 421 gr
  • ISBN-10: 3519022052
  • Publisher Date: 01 Oct 1977
  • Binding: Paperback
  • Language: German
  • Returnable: Y
  • Spine Width: 12 mm
  • Width: 170 mm


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