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Matematicheskie Zametki, 2007, Volume 81, Issue 2, Pages 184–192
DOI: https://doi.org/10.4213/mzm3546 (Mi mzm3546) 		 
Fourier Coefficients of Functions with a Given Modulus of Continuity

V. S. Biryukova

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm3546
Abstract: In this paper, we study the role of the convexity condition for the modulus of continuity in the problem of finding an upper bound for the Fourier coefficients taken over the class of functions with a given modulus of continuity. Also, we solve the problem of the Fourier coefficients for the Rademacher system.
Keywords: Fourier coefficient, modulus of continuity of a function, system of Rademacher functions, $2\pi$-periodic function, convex function.
Received: 11.05.2006
English version:
Mathematical Notes, 2007, Volume 81, Issue 2, Pages 164–171
DOI: https://doi.org/10.1134/S0001434607010191
Bibliographic databases:
UDC: 517.518.454
Language: Russian
Citation: V. S. Biryukova, “Fourier Coefficients of Functions with a Given Modulus of Continuity”, Mat. Zametki, 81:2 (2007), 184–192; Math. Notes, 81:2 (2007), 164–171
Citation in format AMSBIB
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