Some classes of functions and Fourier coefficients with respect to general orthonormal systems

Some classes of functions and Fourier coefficients with respect to general orthonormal systems

The a.e. convergence of an orthogonal series on [0, 1] depends strongly on the coefficients of this series. It is well known that a sufficient condition for the a.e. convergence of such a series is given by the Men’shov-Rademacher theorem. On the other hand, S. Banach proved that good differential p...

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Veröffentlicht in:Proceedings of the Steklov Institute of Mathematics 2013-04, Vol.280 (1), p.156-168
Hauptverfasser: Gogoladze, L., Tsagareishvili, V.
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Mathematics and Statistics
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description The a.e. convergence of an orthogonal series on [0, 1] depends strongly on the coefficients of this series. It is well known that a sufficient condition for the a.e. convergence of such a series is given by the Men’shov-Rademacher theorem. On the other hand, S. Banach proved that good differential properties of a function do not guarantee the a.e. convergence on [0, 1] of the Fourier series of this function with respect to general orthonormal systems (ONSs). In the present study, we find conditions on the functions of an ONS under which the Fourier coefficients of functions of some differential classes satisfy the hypothesis of the Men’shov-Rademacher theorem.
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title Some classes of functions and Fourier coefficients with respect to general orthonormal systems
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