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Eigenvalues of Weakly Singular Integral-Operators

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Cobos, Fernando and Kühn, Thomas (1990) Eigenvalues of Weakly Singular Integral-Operators. Journal of the London Mathematical Society. Second Series, 41 (2). pp. 323-335. ISSN 0024-6107

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Official URL: http://jlms.oxfordjournals.org/content/s2-41/2/323.full.pdf+html


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Abstract

We determine the asymptotic order of decay of eigenvalues of weakly singular integral operators. The singularities are of quite general form, containing power and logarithmic terms. We give a unified elementary proof of all known results in this area. Our approach applies also in the case where the power order of the singularity is equal to the dimension of the domain and the logarithmic order is less than — 1. This case has not been considered previously. Furthermore, we show the optimality of the upper estimates
in a rather strong sense. In particular, we give a partial positive answer to the conjecture of [3].


Item Type:Article
Uncontrolled Keywords:Asymptotic order of decay of eigenvalues of weakly singular integral operators; optimal asymptotic behaviour of eigenvalues
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:15385
Deposited On:28 May 2012 08:45
Last Modified:20 Jun 2018 11:28

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