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Hilberttransformation, Gebrochene Integration Und Differentiation by Paul L. Butzer, Walter Trebels

Hilberttransformation, Gebrochene Integration Und Differentiation

by Paul L. Butzer , Walter Trebels
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Book cover type: Paperback
  • ISBN13: 9783663063445
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Vieweg+teubner Verlag
  • Publisher Imprint: Vieweg+teubner Verlag
  • Publication Date:
  • Pages: 84
  • Original Price: EUR 51.39
  • Language: German
  • Edition: 1968
  • Item Weight: 155 grams
  • BISAC Subject(s): General

Diese Monographie behandelt die eindimensionale Hilberttransformation und die ge- brochene Integration auf der reellen Zahlengeraden. Da sich viele der Beweise auf die Fouriertransformation für Lp-Funktionen (1 P 2) stützen, haben wir in Kapitel 1 alles Nötige aus der Theorie der Fouriertransformation für Funktionen einer Veränder- lichen systematisch zusammengestellt. Weiterhin haben wir uns erlaubt, die wohl- bekannten Eigenschaften der Hilberttransformation ohne Beweis vorauszusetzen und weniger bekannte ausführlich zu beweisen. Der Schwerpunkt der Monographie liegt bei den Kapiteln 3-6, deren Ergebnisse zum gro en Teil neu sind. Da in der Einleitung über die Problemstellung und über die Resultate näher berichtet wird, sei an dieser Stelle nur erwähnt, da Ausgangspunkte unserer Überlegungen Arbeiten folgender Mathematiker sind: S. BOCHNER, J. L. B. COOPER, W. FELLER, G. H. HARDY, J. E. LITTLEWOOD, G. O. OKIKIOLU, M. RIESZ, E. C. TITCHMARSH und H. WEYL. Dadurch wird eine Einordnung unserer Ergebnisse gewährleistet. Unser besonderer Dank gilt Herrn Professor J. L. B. COOPER für viele fruchtbare Dis- kussionen und wertvolle Ratschläge. Seine Vorträge im Aachener Kolloquium und seine Teilnahme an einer Tagung, die der erstgenannte Verfasser im MATHEMATISCHEN FORSCHUNGSINSTITUT OBERWOLFACH im August 1963 abgehalten hat, waren stets an- regend. Die Verfasser danken den Herrn Dr. E. GÖRLICH und H. JOHNEN für manche kritischen Bemerkungen und für ihre Mithilfe bei der Durchsicht von Teilen des Manuskripts und der Korrekturen, ferner Frl. K. REIMER-KELLNER, die das Manuskript mit gro er Sorgfalt geschrieben hat, und dem Westdeutschen Verlag für sein Ent- gegenkommen und die gute Ausstattung dieser Monographie.

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