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Equiconvergence of expansions in eigenfunctions of Sturm-Liouville operators with distributional potentials in Hölder spaces

  • Ordinary Differential Equations
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Abstract

We establish the equiconvergence of expansions of an arbitrary function in the class L 2(0, π) in the Fourier series in sines and in the Fourier series in the eigenfunctions of the first boundary value problem for the one-dimensional Schrödinger operator with a nonclassical potential. The equiconvergence is studied in the norm of the Hölder space. The potential is the derivative of a function that belongs to a fractional-order Sobolev space.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    I. V. Sadovnichaya

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  1. I. V. Sadovnichaya
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Original Russian Text © I.V. Sadovnichaya, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 5, pp. 674–685.

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Sadovnichaya, I.V. Equiconvergence of expansions in eigenfunctions of Sturm-Liouville operators with distributional potentials in Hölder spaces. Diff Equat 48, 681–692 (2012). https://doi.org/10.1134/S0012266112050060

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