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This article is cited in 20 scientific papers (total in 20 papers)
Convergence of eigenfunction expansions at points of discontinuity of the coefficients of a differential operator
V. A. Il'in M. V. Lomonosov Moscow State University
Abstract:
The question of the convergence of expansions in the eigenfunctions of a differential operator with discontinuous coefficients at a point $x_0$ of discontinuity of the coefficients is studied. Given an arbitrary function $f(x)$ in the class $L_2$, a corresponding function $\widetilde f_{x_0}(x)$ is constructed which is such that at the point $x_0$ the eigenfunction expansion of $f(x)$ diverges with the expansion of $\widetilde f_{x_0}(x)$ into a Fourier trigonometric series.
Received: 18.04.1977
Citation:
V. A. Il'in, “Convergence of eigenfunction expansions at points of discontinuity of the coefficients of a differential operator”, Mat. Zametki, 22:5 (1977), 679–698; Math. Notes, 22:5 (1977), 870–882
Linking options:
https://www.mathnet.ru/eng/mzm8092 https://www.mathnet.ru/eng/mzm/v22/i5/p679
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Abstract page: | 336 | Full-text PDF : | 143 | First page: | 1 |
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