Convergence of the Spectral Expansion in the Eigenfunctions of a Fourth-Order Differential Operator

We study the convergence of spectral expansions of functions of the class W p 1 ( G ), p ≥ 1, G = (0, 1), in the eigenfunctions of an ordinary differential operator of even order with integrable coefficients. Sufficient conditions for absolute and uniform convergence are obtained and the rate of uni...

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Bibliographic Details
Published in:Differential equations 2019, Vol.55 (1), p.8-23
Main Authors: Kurbanov, V. M., Godzhaeva, Kh. R.
Format: Article
Language:English
Subjects:
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
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Summary:We study the convergence of spectral expansions of functions of the class W p 1 ( G ), p ≥ 1, G = (0, 1), in the eigenfunctions of an ordinary differential operator of even order with integrable coefficients. Sufficient conditions for absolute and uniform convergence are obtained and the rate of uniform convergence of these expansions on the interval ̅G is found.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266119010026