On the eigenvalues and eigenfunctions of some integral operators

Some properties of the eigenvalues of the integral operator K gt defined as K τ f( x) = ∫ 0 τ K( x − y) f ( y) dy were studied by Vittal Rao ( J. Math. Anal. Appl. 53 (1976) , 554–566), with some assumptions on the kernel K( x). In this paper the eigenfunctions of the operator K τ are shown to be co...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 109; no. 2; pp. 463 - 471
Main Authors Rao, R.Vittal, Sukavanam, N
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.08.1985
Elsevier
Subjects
Exact sciences and technology
Function theory, analysis
Mathematical methods in physics
Physics
Eigenvalue
Integral operator
Eigenfunction
Mathematical operator
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Summary:Some properties of the eigenvalues of the integral operator K gt defined as K τ f( x) = ∫ 0 τ K( x − y) f ( y) dy were studied by Vittal Rao ( J. Math. Anal. Appl. 53 (1976) , 554–566), with some assumptions on the kernel K( x). In this paper the eigenfunctions of the operator K τ are shown to be continuous functions of τ under certain circumstances. Also, the results of Vittal Rao and the continuity of eigenfunctions are shown to hold for a larger class of kernels.
ISSN:0022-247X
1096-0813
DOI:10.1016/0022-247X(85)90162-3