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Problems of Unconditional Convergence

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Abstract

S. Banach proved that for a function, even with good differentiability properties, the convergence of its Fourier series with respect to the general orthonormal systems (ONS) is not guaranteed. In the present paper, we find conditions on the functions of an ONS, under for which the Fourier series of differentiable functions are a.e. unconditionally convergent. The obtained results are best possible. We also prove that any ONS contains a subsystem such that the Fourier series of any function with derivatives of bounded variation are unconditionally convergent a.e. on [0, 1].

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Authors and Affiliations

  1. Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    V. Tsagareishvili

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  1. V. Tsagareishvili
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Correspondence to V. Tsagareishvili.

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Tsagareishvili, V. Problems of Unconditional Convergence. Anal Math 48, 1213–1229 (2022). https://doi.org/10.1007/s10476-022-0173-3

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  • DOI: https://doi.org/10.1007/s10476-022-0173-3

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