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ASYMPTOTIC BEHAVIOUR OF EIGENVALUES OF CERTAIN POSITIVE INTEGRAL OPERATORS

Published online by Cambridge University Press:  01 January 2009

YÜKSEL SOYKAN*
Affiliation:
Department of Mathematics, Art and Science Faculty, Zonguldak Karaelmas University, 67100, Zonguldak, Turkey e-mail: yuksel_soykan@hotmail.com
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Abstract

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In this paper, we prove a theorem concerning asymptotic estimates of the eigenvalues of certain positive integral operators with Laplace transform type kernels.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Gohberg, I., Goldberg, S. and Kaashoek, M. A., Basic classes of linear operators (Birkhauser Verlag AG, Basel, Switzerland, 2003).CrossRefGoogle Scholar
2.Little, G. and Reade, J. B., Eigenvalues of analytic kernels, SIAM J. Math. Anal. 15 (1984), 133136.CrossRefGoogle Scholar
3.Little, G., Asymptotic estimates of the eigenvalues of certain positive Fredholm operators II, Proc. Camb. Philos. Soc. 101 (1987), 535545.CrossRefGoogle Scholar
4.Little, G., Equivalences of positive integral operators with rational kernels, Proc. London Math. Soc. 62 (1991), 403426.CrossRefGoogle Scholar
5.Little, G., Eigenvalues of positive power series kernels, Bull. London Math. Soc. 28 (1996), 4350.CrossRefGoogle Scholar
6.Riesz, F. and Sz-Nagy, B., translated by Boron, L. F., Functional analysis (Frederick Ungar Publishing Co., New York, 1955).Google Scholar
7.Rosenblum, G., Solomiak, M. and Shubin, M., Encyclopaedia of mathematical sciences, Vol. 64. Partial differential equations. VII. Spectral theory of differential operators, (Springer Verlag, Berlin Heidelberg, 1994).Google Scholar
8.Soykan, Y., Integral operators with analytic kernels, PhD Thesis (University of Manchester, Manchester, UK., 2000).Google Scholar
9.Widom, H., Asymptotic behaviour of the eigenvalues of certain integral equations, Arch. Ration. Mech. Anal. 17 (1964), 215229.CrossRefGoogle Scholar