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Dependence of estimates of the local convergence rate of spectral expansions on the distance from an interior compact set to the boundary

  • ordinary differential Equations
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Abstract

We consider the problem on the convergence rate of biorthogonal expansions of functions in systems of root functions of a wide class of ordinary second-order differential operators defined on a finite interval. These expansions are compared with expansions of the same functions in Fourier trigonometric series in an integral or uniform metric on any interior compact subset of the main interval. We find the dependence of the equiconvergence rate of resulting expansions on the distance from the compact set to the boundary of the interval, on the coefficients of the differential operation, and on the presence of infinitely many associated functions in the system of root functions.

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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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Original Russian Text © I.S. Lomov, 2010, published in Differentsial’nye Uravneniya, 2010, Vol. 46, No. 10, pp. 1409–1420.

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Lomov, I.S. Dependence of estimates of the local convergence rate of spectral expansions on the distance from an interior compact set to the boundary. Diff Equat 46, 1415–1426 (2010). https://doi.org/10.1134/S0012266110100058

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  • DOI: https://doi.org/10.1134/S0012266110100058

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