Geodesic
General orthonormal systems and absolute convergence
Izvestiya. Mathematics , Tome 84 (2020) no. 4, pp. 816-828

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We study problems of the absolute convergence of Fourier series of differentiable functions with respect to general orthonormal systems (ONS). We obtain results which show that under certain conditions on functions in the ONS, the Fourier series of an arbitrary function in a certain differentiability class is absolutely convergent. We finally note that our results cannot be improved.
Keywords: orthonormal system, absolute convergence of Fourier series, function of bounded variation.
Mots-clés : Fourier coefficients 
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     author = {V. Sh. Tsagareishvili},
     title = {General orthonormal systems and absolute convergence},
     journal = {Izvestiya. Mathematics },
     pages = {816--828},
     publisher = {mathdoc},
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     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2020_84_4_a9/}
}
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V. Sh. Tsagareishvili. General orthonormal systems and absolute convergence. Izvestiya. Mathematics , Tome 84 (2020) no. 4, pp. 816-828. http://geodesic.mathdoc.fr/item/IM2_2020_84_4_a9/