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Absolute convergence of fourier series of almost-periodic functions

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Abstract

We present necessary and sufficient conditions for the absolute convergence of the Fourier series of almost-periodic (in the sense of Besicovitch) functions when the Fourier exponents have limit points at infinity or at zero. The structural properties of the functions are described by the modulus of continuity or the modulus of averaging of high order, depending on the behavior of the Fourier exponents. The case of uniform almost-periodic functions of bounded variation is considered.

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Authors and Affiliations

  1. Russo-Tajik Slavic University, Dushanbe, Tajikistan

    Yu. Kh. Khasanov

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  1. Yu. Kh. Khasanov
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Correspondence to Yu. Kh. Khasanov.

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Original Russian Text © Yu. Kh. Khasanov, 2013, published in Matematicheskie Zametki, 2013, Vol. 94, No. 5, pp. 745–756.

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Khasanov, Y.K. Absolute convergence of fourier series of almost-periodic functions. Math Notes 94, 692–702 (2013). https://doi.org/10.1134/S0001434613110102

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  • DOI: https://doi.org/10.1134/S0001434613110102

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