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Reihen von Funktionen

In: Lehrbuch der Funktionentheorie

Author

Listed:
  • Hans Hornich

    (Technischen Hochschule Graz)

Abstract

Zusammenfassung Bereits im Anfang haben wir gezeigt, daß eine gleichmäßig konvergente Reihe von stetigen Funktionen wieder stetig ist. Ein analoger Satz für differenzierbare Funktionen ist im Reellen nicht richtig: eine gleichmäßig konvergente Reihe von differenzierbaren Funktionen ist i. a. nicht differenzierbar: man denke nur an gleichmäßig konvergente Fouriersche Reihen, die eine Kurve mit Ecken darstellen, also nicht cfferenzierbar sind. Dagegen gilt ein solcher Satz im Komplexen; es ist dies der sogenannte Doppelreihensatz von Weierstraβ, der auf Grund der bisher gewonnenen Resultate äußerst einfach zu beweisen ist.

Suggested Citation

  • Hans Hornich, 1950. "Reihen von Funktionen," Springer Books, in: Lehrbuch der Funktionentheorie, chapter 0, pages 107-124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-7739-6_7
    DOI: 10.1007/978-3-7091-7739-6_7
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