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The Fourier transformation of functions defined on a Hilbert space

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Abstract

It is shown that one cannot define a transformation analogous to the Fourier transformation, carrying a function into a function, for functions defined on a Hilbert space.

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Literature cited

  1. V. I. Averbukh, O. G. Smolyanov, and S. V. Fomin, “Generalized functions and differential equations in linear spaces,” Tr. Mosk. Matem. Ob-va,24, 133–174 (1971).

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  2. I. M. Gel'fand and N. Ya. Vilenkin, Generalized Functions, Vol. 4, Applications of Harmonic Analysis, Academic Press, New York (1964).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    V. Yu. Bentkus

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  1. V. Yu. Bentkus
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Additional information

Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 465–468, October, 1973.

I am grateful to O. G. Smolyanov for constant interest.

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Bentkus, V.Y. The Fourier transformation of functions defined on a Hilbert space. Mathematical Notes of the Academy of Sciences of the USSR 14, 825–826 (1973). https://doi.org/10.1007/BF01108805

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  • DOI: https://doi.org/10.1007/BF01108805

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