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Equiconvergence theorems for singular Sturm-Liouville operators with various boundary conditions

  • Ordinary Differential Equations
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Abstract

We consider the Sturm-Liouville operator L(y) = −d 2 y/dx 2 + q(x)y in the space L 2[0, π], where the potential q(x) is a complex-valued distribution of the first order of singularity; namely, q(x) = ut’(x), where u ∈ L 2[0, π]. (The derivative is understood in the sense of distributions.) We study the uniform equiconvergence on the entire interval [0, π] of the expansions of a function f ∈ L 2 in the system of eigenfunctions and associated functions of the operator L with the Fourier trigonometric series expansion. We also estimate the equiconvergence rate.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    O. A. Shveikina

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  1. O. A. Shveikina
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Correspondence to O. A. Shveikina.

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Original Russian Text © O.A. Shveikina, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 2, pp. 174–182.

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Shveikina, O.A. Equiconvergence theorems for singular Sturm-Liouville operators with various boundary conditions. Diff Equat 51, 177–185 (2015). https://doi.org/10.1134/S0012266115020032

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  • DOI: https://doi.org/10.1134/S0012266115020032

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