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The variation of general Fourier coefficients of Lipschitz class functions

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Abstract

We investigate the behaviour of the series of moduli of differences of the Fourier coefficients of functions from a certain functional class. We consider general orthonormal systems (ONS), their subsystems, general Fourier coefficients of the function with respect to these subsystems and classical systems (trigonometric, Haar and Walsh systems). It is shown that in order to obtain the known results for a general ONS, we need to impose special conditions on the functions of the given ONS. The obtained results are best possible.

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References

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  1. Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, 13 University Str., Tbilisi, 0186, Georgia

    V. Tsagareishvili

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  1. V. Tsagareishvili
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Correspondence to V. Tsagareishvili.

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Tsagareishvili, V. The variation of general Fourier coefficients of Lipschitz class functions. Acta Math. Hungar. 166, 142–161 (2022). https://doi.org/10.1007/s10474-022-01213-6

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  • DOI: https://doi.org/10.1007/s10474-022-01213-6

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