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On the Optimal Asymptotic Eigenvalue Behavior of Weakly Singular Integral-Operators

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http://www.jstor.org/stable/2048778 .
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Publication Date
1991
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American Mathematical Society
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Abstract
We improve the known results on eigenvalue distributions of weakly singular integral operators having (power) order of the singularity equal to half of the dimension of the underlying domain. Moreover we show that our results are the best possible.
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Análisis funcional y teoría de operadores
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B. Carl and T. Kuhn, Entropy and eigenvalues of certain integral operators, Math. Ann. 268 (1984), 127-136. F. Cobos and T. Kuhn, Entropy and eigenvalues of weakly singular integral operators, Inte-gral Equations and Operator Theory 11 (1988), 64-86. - Eigenvalues of weakly singular integral operators, J. London Math. Soc. (2) 41 (1990), 323-335. I. C. Gohberga nd M. G. Krein, Introductiont o the theoryo f linear non-selfadjoint operators, Amer. Math. Soc., Providence, RI, 1969. H. Konig, Some remarks on weakly singular integral operators, Integral Equations and Operator Theory 3 (1980), 397-407. -Eigenvalue distribution of compact operators, Birkhauser, Basel, Boston, MA, and Stuttgart, 1986. H. Konig, J. R. Retherford, and N. Tomczak-Jaegermann, On the eigenvalueso f (p, 2)- summing operators and constants associated to normed spaces, J. Funct. Anal. 37 (1980), 88-126. G. P. Kostometov, Asymptotic behaviour of the spectrum of integral operators with a singu-larity on the diagonal, Math. USSR-Sb. 23 (1974), 417-424.
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https://hdl.handle.net/20.500.14352/57282
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