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On Fourier transforms of functions of bounded type in tubular domains

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Abstract

We obtain a necessary and sufficient condition in terms of the Fourier transform under which an analytic function of bounded type in a tubular domain belongs to the Hardy class H 1(ℂ+ n).

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References

  1. Duren P., Theory of H p Spaces, Academic Press, New York (1970).

    MATH  Google Scholar 

  2. Garnett J., Bounded Analytic Functions, Academic Press, New York (1981).

    MATH  Google Scholar 

  3. Rudin W., Function Theory in Polydisks, W. A. Benjamin, Inc., New York and Amsterdam (1969).

    Google Scholar 

  4. Bochner S. and Martin W. T., Functions of Several Variables [Russian translation], Izdat. Inostr. Lit., Mir (1951).

    Google Scholar 

  5. Paley R. and Wiener N., Fourier Transforms in the Complex Domain [Russian translation], Nauka, Moscow (1964).

    MATH  Google Scholar 

  6. Shamoyan F. A., “On Fourier transforms of functions of the R. Nevanlinna class in the half-plane,” St. Petersburg Math. J., 20, No. 4, 665–680 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  7. Shamoyan F. A., “Characterization of the rate of decay for the Fourier coefficients of functions of bounded form and the classes of analytic functions with infinitely differentiable boundary values,” Sib. Math. J., 36, No. 4, 816–826 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  8. Vladimirov V. S., Generalized Functions in Mathematical Physics [Russian], Nauka, Moscow (1979).

    MATH  Google Scholar 

  9. Hörmander L., The Analysis of Linear Partial Differential Operators. Vol. 1: Distribution Theory and Fourier Analysis [Russian translation], Mir, Moscow (1986).

    MATH  Google Scholar 

  10. Hörmander L., An Introduction to Complex Analysis in Several Variables [Russian translation], Mir, Moscow (1968).

    MATH  Google Scholar 

  11. Koosis P., The Logarithmic Integral. I, Cambridge Univ. Press, Cambridge (1988).

    Book  MATH  Google Scholar 

  12. Mergelyan S. N., “Weighted approximation by polynomials,” Uspekhi Mat. Nauk, 11, No. 5, 102–152 (1956).

    MathSciNet  Google Scholar 

  13. Ronkin L. I., Introduction to the Theory of Entire Functions of Several Variables, Amer. Math. Soc., Providence (1974).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Bryansk State University, Bryansk, Russia

    F. A. Shamoyan

Authors
  1. F. A. Shamoyan
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Correspondence to F. A. Shamoyan.

Additional information

Original Russian Text Copyright © 2016 Shamoyan F.A.

The author was supported by the Ministry of Education and Science of the Russian Federation (Grant 1.1704.2014K) and the Russian Foundation for Basic Research (Grant 13–01–97508).

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Shamoyan, F.A. On Fourier transforms of functions of bounded type in tubular domains. Sib Math J 57, 1100–1116 (2016). https://doi.org/10.1134/S0037446616060173

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