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Teilmengen von Funktionenräumen

In: Lineare Funktionalanalysis

Author

Listed:
  • Hans Wilhelm Alt

    (Institut für Angewandte Mathematik, Abteilung für Funktionalanalysis und Numerische Mathematik)

Abstract

Zusammenfassung In diesem Abschnitt betrachten wir Teilmengen mit speziellen Eigenschaften der in Abschnitt 1 eingeführten Funktionenräume. Zwei grundlegende Eigenschaften, mit deren Hilfe man in Anwendungen z. B. Existenzaussagen für partielle Differentialgleichungen herleitet, sind die Konvexität bzw. die Kompaktheit. Wir betrachten zunächst konvexe Teilmengen (siehe 2.1–2.3) und beweisen insbesondere den Projektionssatz im Hilbertraum. Anschließend untersuchen wir kompakte Teilmengen metrischer Räume (siehe 2.5–2.15) und geben vollständige Charakterisierungen kompakter Mengen in C 0- und L P -Räumen an (siehe 2.11 und 2.15). Auf diese Charakterisierungen wird in Anwendungen häufig zurückgegriffen.

Suggested Citation

  • Hans Wilhelm Alt, 1999. "Teilmengen von Funktionenräumen," Springer Books, in: Lineare Funktionalanalysis, edition 0, chapter 2, pages 83-124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-08387-1_4
    DOI: 10.1007/978-3-662-08387-1_4
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