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Ein Beweis Des Satzes von Plancherel

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Zusammenfassung

Man betrachtet für eine Funktion ϕ(x)∈L 2(−π, π) die vom Parameter α abhängige Entwicklung\(\varphi (x) = \frac{1}{{\sqrt {2\pi } }}\sum\limits_{k = - \infty }^\infty {(F_\varphi )(\alpha + k)e^{ - ix(\alpha + k)} } \). Durch Integration nach α wird es möglich, von den Fourierreihen zur Fouriertransformation zu gelangen und den Satz von Plancherel zu beweisen.

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Literatur

  1. Burkill J. C.,The Lebesgue Integral, Cambridge Tracts in Mathematics and Mathematical Physics No. 40, Cambridge University Press 1953.

  2. Katznelson Y.,An introduction to Harmonic Analysis, New York-London-Sydney-Toronto, John Wiley & Sons, Inc. 1968.

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  3. Sz.-Nagy B.,Introduction to Real Functions and Orthogonal Expansions, Joint edition published by, Akadémiai Kiadó, Budapest and Oxford University Press, New York 1964.

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Authors and Affiliations

  1. Solothurn, Schweiz

    Antonio Steiner

Authors
  1. Antonio Steiner
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Additional information

Vorgestellt von Herrn Prof. R. Nevanlinna.

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Steiner, A. Ein Beweis Des Satzes von Plancherel. Rend. Circ. Mat. Palermo 21, 25–30 (1972). https://doi.org/10.1007/BF02844228

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  • DOI: https://doi.org/10.1007/BF02844228

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