Eigenvalues of analytic kernels

It is shown that the eigenvalues of an analytic kernel on a finite interval go to zero at least as fast as $R^{ - n} $ for some fixed $R < 1$. The best possible value of $R$ is related to the domain of analyticity of the kernel. The method is to apply the Weyl-Courant minimax principle to the tai...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 1984, Vol.15 (1), p.133-136
Main Authors: LITTLE, G, READE, J. B
Format: Article
Language:English
Subjects:
Eigenvalues
Exact sciences and technology
Function theory, analysis
Mathematical methods in physics
Physics
Polynomials
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Summary:It is shown that the eigenvalues of an analytic kernel on a finite interval go to zero at least as fast as $R^{ - n} $ for some fixed $R < 1$. The best possible value of $R$ is related to the domain of analyticity of the kernel. The method is to apply the Weyl-Courant minimax principle to the tail of the Chebyshev expansion for the kernel. An example involving Legendre polynomials is given for which $R$ is critical.
ISSN:0036-1410
1095-7154
DOI:10.1137/0515009