Abstract
Banach [1] proved that good differential properties of function do not guarantee the a.e. convergence of the Fourier series of this function with respect to general orthonormal systems (ONS). On the other hand it is very well known that a sufficient condition for the a.e. convergence of an orthonormal series is given by the Menshov–Rademacher Theorem. The paper deals with sequence of positive numbers \((d_{n})\) such that multiplying the Fourier coefficients \((C_{n}(f))\) of functions with bounded variation by these numbers one obtains a.e. convergent series of the form \(\sum_{n=1}^{\infty}d_{n}C_{n}(f)\varphi_{n}(x).\) It is established that the resulting conditions are best possible.
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The research was supported by Shota Rustaveli National Science Foundation, grant no. FR-19-676.
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MSC2010 numbers: 42C10; 46B07
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Tsagareishvili, V., Tutberidze, G. Some Problems of Convergence of General Fourier Series. J. Contemp. Mathemat. Anal. 57, 369–379 (2022). https://doi.org/10.3103/S1068362322060085
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DOI: https://doi.org/10.3103/S1068362322060085