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General Fourier coefficients and convergence almost everywhere. (English. Russian original) Zbl 1464.42002

Izv. Math. 85, No. 2, 228-240 (2021); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 85, No. 2, 60-72 (2021).
Summary: We find sufficient conditions which are in a sense best possible that must be satisfied by the functions of an orthonormal system \((\varphi_n)\) in order for the Fourier coefficients of functions of bounded variation to satisfy the hypotheses of the Men’shov-Rademacher theorem. We also prove a theorem saying that every system \((\varphi_n)\) contains a subsystem \((\varphi_{n_k})\) with respect to which the Fourier coefficients of functions of bounded variation satisfy those hypotheses. The results obtained complement and generalize the corresponding results in [L. Gogoladze and V. Tsagareishvili, Proc. Steklov Inst. Math. 280, 156–168 (2013; Zbl 1293.42029); translation from Tr. Mat. Inst. Steklova 280, 162–174 (2013)].

MSC:

42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
42A20 Convergence and absolute convergence of Fourier and trigonometric series

Citations:

Zbl 1293.42029
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References:

[1] Gogoladze L. and Tsagareishvili V. 2013 Some classes of functions and Fourier coefficients with respect to general orthonormal systems Trudy MIAN280 162-174 · Zbl 1293.42029 · doi:10.1134/S0081543813010100
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