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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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 .
|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|
B. CARL and T. KUHN, 'Entropy and eigenvalues of certain integral operators', Math. Ann. 268 (1984) 127-136.
B. CARL and T. KUHN, ' Local entropy moduli and eigenvalues of operators in Banach spaces', Rev. Mat. Hisp.-Amer. (4) 1 (1985) 127-148.
F. COBOS and T. KUHN, 'Entropy and eigenvalues of weakly singular integral operators', Integral Equations Operator Theory 11 (1988) 64-86.
I. C. GOHBERG and M. G. KREIN, Introduction to the theory of linear non-selfadjoint operators (American Mathematical Society, Providence, 1969).
H. KONIG, 'Weyl-type inequalities for operators in Banach spaces', Proceedings, Conference on Functional Analysis, Paderborn 1979, Mathematics Studies 38 (North-Holland, Amsterdam, 1980) 297-317.
H. KONIG, ' Some remarks on weakly singular integral operators', Integral Equations Operator Theory(1980) 397-407.
H. KONIG, Eigenvalue distribution of compact operators (Birkhauser, Basel, 1986).
H. KONIG, J. R. RETHERFORD and N. TOMCZAK-JAEGERMANN, 'On the eigenvalues of (p,2)-summing operators and constants associated to normed spaces', J. Fund. Anal. 37 (1980) 88—126.
G. P. KOSTOMETOV, 'Asymptotic behaviour of the spectrum of integral operators with a singularity on the diagonal', Math. USSR Sb. 23 (1974) 417-424.
A. PIETSCH, Eigenvalues and s-numbers (University Press, Cambridge, 1987).
|Deposited On:||28 May 2012 10:45|
|Last Modified:||22 Oct 2013 15:54|
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