General Fourier coefficients and summability a.e

Author: Giorgi Cagareishvili
Keywords: Fourier coefficients, orthonormal systems, summability, functions of bounded variation
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In this paper we investigate sufficient conditions which are satisfied by general orthonormal system functions, so that Fourier coefficients of bounded variation functions satisfy the condition of the Menshov theorem. The obtained result is the best possible in a certain sense. We also prove a theorem, which shows that any orthonormal system contains a subsystem for which the Fourier series of any bounded variation functions are summable a.e by method of Cessaro. The obtained results generalize the relevant results from the known paper.