, Volume 48, Issue 8, pp 1090-1102

Estimates for the equiconvergence rate of spectral expansions on an interval

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Abstract

We study the convergence rate of biorthogonal expansions of functions in series in systems of root functions of a broad class of second-order ordinary differential operators on a finite interval. The above-mentioned expansions are compared with the expansions of the same functions in trigonometric Fourier series in an integral or uniform metric on any interior compact set of the basic interval and on the entire interval. We prove the dependence of the equiconvergence rate of the expansions in question 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.

Original Russian Text © A.S. Markov, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 8, pp. 1105–1116.