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Convergence of spectral expansions for functions of the hölder class for two problems with a spectral parameter in the boundary condition

Convergence of spectral expansions for functions of the hölder class for two problems with a... Differential Equations, Vol. 36. No. 8, 2000, pp. 1182-1188. Translated from Differentsial'nye Uravneniya, Vol. 36, No. 8, 2000, pp. 1069-1074. Original Russian Text Copyright @ 2000 by Kapustin, Aloiseev. PARTIAL DIFFERENTIAL EQUATIONS Convergence of Spectral Expansions for Functions of the HSlder Class for Two Problems with a Spectral Parameter in the Boundary Condition N. Yu. Kapustin and E. I. Moiseev Moscow State University, Moscow, Russia Computer Center, Russian Academy of Sciences, Moscow, Russia Received February 18, 2000 We consider two spectral problems that appear in a model of a transrelaxation heat process and in the mathematical description of vibrations of a loaded string. We study the uniform convergence of spectral expansions of H61der class functions in the entire domain. Consider the spectral problem u"(x) + Au(x) = 0, (1) ~(1) = 0, (a - X)~'(0) + ab~(0) = 0, a,b > 0, (2) which has only the eigenfunctions u~(x) = v~sin(v/~(1-x)), n = 0,1,2,..., with positive eigenvalues determined by the equation tan v~ = (a - A)/(bv~). The zero index is assigned to an arbitrary eigenfunction, and all remaining eigenfunctions are numbered in ascending order of the corresponding eigenvalues. The following assertions were proved in [1]. Lemma 1. The http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Convergence of spectral expansions for functions of the hölder class for two problems with a spectral parameter in the boundary condition

Kapustin, N.; Moiseev, E.
Differential Equations , Volume 36 (8) – Nov 15, 2007
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Publisher
Springer Journals
Copyright
Copyright © 2000 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/BF02754186
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 36. No. 8, 2000, pp. 1182-1188. Translated from Differentsial'nye Uravneniya, Vol. 36, No. 8, 2000, pp. 1069-1074. Original Russian Text Copyright @ 2000 by Kapustin, Aloiseev. PARTIAL DIFFERENTIAL EQUATIONS Convergence of Spectral Expansions for Functions of the HSlder Class for Two Problems with a Spectral Parameter in the Boundary Condition N. Yu. Kapustin and E. I. Moiseev Moscow State University, Moscow, Russia Computer Center, Russian Academy of Sciences, Moscow, Russia Received February 18, 2000 We consider two spectral problems that appear in a model of a transrelaxation heat process and in the mathematical description of vibrations of a loaded string. We study the uniform convergence of spectral expansions of H61der class functions in the entire domain. Consider the spectral problem u"(x) + Au(x) = 0, (1) ~(1) = 0, (a - X)~'(0) + ab~(0) = 0, a,b > 0, (2) which has only the eigenfunctions u~(x) = v~sin(v/~(1-x)), n = 0,1,2,..., with positive eigenvalues determined by the equation tan v~ = (a - A)/(bv~). The zero index is assigned to an arbitrary eigenfunction, and all remaining eigenfunctions are numbered in ascending order of the corresponding eigenvalues. The following assertions were proved in [1]. Lemma 1. The

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Differential Equations – Springer Journals

Published: Nov 15, 2007

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