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Summability of Fourier series for almost-periodic functions on locally compact Abelian groups

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Abstract

Some results concerning the summability of Fourier series of continuous 2π-periodic functions are generalized for the case of almost-periodic functions defined on locally compact Abelian groups.

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References

  1. Levitan, B.M. Almost-Periodic Functions (Gostekhizdat, Moscow, 1953) [in Russian].

    MATH  Google Scholar 

  2. Ugulava, D. On the Approximation of Functions on Locally Compact Abelian Groups, GeorgianMath. J. 6, No. 4, 379–399 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  3. Ugulava, D. Approximation of Functions on Locally Compact Abelian Groups, GeorgianMath. J. 19, No. 1, 181–193 (2012).

    MathSciNet  MATH  Google Scholar 

  4. Ugulava, D. On Some Approximation Properties of a Generalized Fejer Integral, Bull. of the Georgian Nat. Acad. of Sciences 6, No. 1, 32–38 (2012).

    MathSciNet  MATH  Google Scholar 

  5. Hewitt, E., Ross, K. A. Abstract Harmonic Analysis. Vol.2. Structure and Analysis for CompactGroups. Analysis on Locally Compact Abelian Groups (Springer-Verlag, Berlin-Heidelberg-New York, 1970; Mir, Moscow, 1987).

    Google Scholar 

  6. Neumann, J. von Almost-Periodic Functions in a Group, Trans. Amer.Math. Soc. 36, No. 3, 445–492 (1934).

    Article  MathSciNet  MATH  Google Scholar 

  7. Struble, R. A. Almost Periodic Functions on Locally Compact Groups, Proc. Nat. Acad. Sci. USA 39, 122–126 (1952).

    Article  MathSciNet  MATH  Google Scholar 

  8. Yoshi, Milan A. and Podhye, S. M. On the Equivalence of Several Definitions of Almost Periodic Functions on Locally Compact Groups, Global Journal of Math. Sci.: Theory and Practical 2, No. 3, 143–149 (2010).

    Google Scholar 

  9. Bredikhina, E.A. Some Problems in Summation of Fourier Series of Almost Periodic Functions, Uspekhi Mat. Nauk 15, No. 5, 143–150 (1960) [in Russian].

    MathSciNet  Google Scholar 

  10. Vladimirov, V. S., Volovich, I. V., and Zelenov, E. I. P-Adic Analyisis and Mathematical Physics (World Scientific, Singapore, 1994).

    Book  MATH  Google Scholar 

  11. Mackey, G. Laplace Transform for Locally Compact Abelian Groups, Proc. Nat. Acad. Sci. USA 34, 158–162 (1948).

    Article  MathSciNet  MATH  Google Scholar 

  12. Ugulava, D. An Analog of the Paley–Wiener theorem, Russian Mathematics 46, No. 8, 62–67 (2002).

    MathSciNet  MATH  Google Scholar 

  13. Bohr, H. Almost-Periodic Functions (Chelsea, New York, 1947).

    MATH  Google Scholar 

  14. Levitan, B. M., Zhikov, V. V. Almost Periodic Functions and Differential Equations (Moscow Univ. Press, 1978; Cambridge Univ. Press, Cambridge, 1982).

    MATH  Google Scholar 

  15. Yudin, V. A. The Approximation of Functions of Many Variables by Their Fejer Sums, Math. Notes 13, No. 6, 490–496 (1973).

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to D. K. Ugulava.

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Original Russian Text © D.K. Ugulava, 2016, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, No. 12, pp. 82–95.

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Ugulava, D.K. Summability of Fourier series for almost-periodic functions on locally compact Abelian groups. Russ Math. 60, 67–78 (2016). https://doi.org/10.3103/S1066369X16120100

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