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Loaded differential operators: Convergence of spectral expansions

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Abstract

We study the convergence rate of biorthogonal series expansions of functions in systems of root functions of a broad class of loaded even-order differential operators defined on a finite interval. These expansions are compared with the Fourier trigonometric series expansions of the same functions in an integral metric on any interior compact set of the main interval or on the entire interval. We obtain estimates for the equiconvergence rate of these expansions.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    I. S. Lomov

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  1. I. S. Lomov
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Correspondence to I. S. Lomov.

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Original Russian Text © I.S. Lomov, 2014, published in Differentsial’nye Uravneniya, 2014, Vol. 50, No. 8, pp. 1077–1086.

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Lomov, I.S. Loaded differential operators: Convergence of spectral expansions. Diff Equat 50, 1070–1079 (2014). https://doi.org/10.1134/S0012266114080060

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