Hilbert-Räume Und Spektralmaße by Siegfried Brehmer
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Hilbert-Räume Und Spektralmaße

Hilbert-Räume Und Spektralmaße


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About the Book

Die Theorie der HILBERT-Raume ist wohl der alteste Zweig der Funktionalanalysis. Sie ist zu Anfang dieses Jahrhunderts durch Abstraktion aus der Theorie der Inte- gralgleichungen erwachsen und findet heute in den ver- schiedensten Bereichen der Mathematik und Naturwissen- schaften vielfaltige Anwendungen. So bildet sie zum Bei- spiel die Grundlage ftir einen axiomatischen Aufbau der Quantenmechanik. Grundkenntnisse tiber die Theorie der HILBERT-Raume sind heute ein unentbehrliches Hilfs- mittel ftir jeden Mathematiker und theoretischen Phy- siker. Innerhalb der Funktionalanalysis zeichnet sich die Theorie der HILBERT-Raume durch groBe Anschaulich- keit aus. Das Vorhandensein einer Metrik und einer Ortho- gonalitatsrelation ermoglicht auch in abstrakten Begriffs- bildungen eine elementargeometrische Betrachtungsweise. Wir haben uns wiederholt bemtiht, solche geometrischen Analogien bewuBt zu machen. Die allgemeinere Theorie der normierten Raume wird nur so weit entwickelt, wie sie ftir Anwendungen innerhalb der Theorie der HILBERT- Raume bedeutungsvoll ist. 1m ersten Kapitel werden die grundlegenden Begriffs- bildungen bereitgestellt. Der Hauptteil des Bandchens ist entsprechend ihrer Bedeutung der Theorie der be- schrankten linearen Operatoren gewidmet. 1m Mittel- punkt steht die Spektralzerlegung beschrankter selbst- adjungierter Operatoren, die in den ersten beiden Ab- schnitten des dritten Kapitels auf unbeschriinkte selbst- adjungierte Operatoren ausgedehnt wird. Der Rest dieses Kapitels bringt eine relativ elementare Einftihrung in die Vorwort 4 allgemeine Theorie der SpektralmaBe und Spektral- integrale und gipfelt in der Bereitstellung des Funktional- kalkiils fiir meBbare Funktionen von unbeschrankten normalen Operatoren. Hierbei werden nur elementare Kenntnisse tiber meBbare Funktionen benotigt, die tiber- dies noch einmal zusammenfasseud dargestellt werden.


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Product Details
  • ISBN-13: 9783528068561
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Edition: 1978 ed.
  • Language: German
  • Returnable: Y
  • Spine Width: 12 mm
  • Width: 127 mm
  • ISBN-10: 3528068566
  • Publisher Date: 01 Jan 1979
  • Binding: Paperback
  • Height: 203 mm
  • No of Pages: 224
  • Series Title: Reihe Wissenschaft
  • Weight: 281 gr


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