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This article is cited in 10 scientific papers (total in 10 papers)
Absolute Convergence of Fourier Series of Almost-Periodic Functions
Yu. Kh. Khasanov Russian-Tajik Slavonic University
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.
Keywords:
almost-periodic function, Fourier series, trigonometric polynomial, function of bounded variation, modulus of continuity, Parseval's inequality.
Received: 17.03.2010 Revised: 05.12.2012
Citation:
Yu. Kh. Khasanov, “Absolute Convergence of Fourier Series of Almost-Periodic Functions”, Mat. Zametki, 94:5 (2013), 745–756; Math. Notes, 94:5 (2013), 692–702
Linking options:
https://www.mathnet.ru/eng/mzm8778https://doi.org/10.4213/mzm8778 https://www.mathnet.ru/eng/mzm/v94/i5/p745
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