Estimation of the closeness of partial sums of expansions in eigenfunctions of a Sturm-Liouville operator with discontinuous coefficients. (Russian. Russian summary)статья
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Аннотация:We establish the orders of closeness with respect to μ as μ → + ∞ of partial sums of order μ of expansions in eigenfunctions of a Sturm-Liouville operator of an absolutely continuous function and an absolutely continuous function with a compact support f(x) and a modified partial sum of order μ of a trigonometric series of a modified function f~ x0 (x) at a point of discontinuity x = x0 of the coefficients of the operator. Based on these results we obtain estimates for the closeness of the partial sums of order μ as μ → + ∞ of expansions of functions of the classes indicated associated with two selfadjoint extensions of Sturm-Liouville operators with discontinuous coefficients at a point x=x 0 of discontinuity of their coefficients.