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A simple test for nuclearity of integral operators on L2(Rn)

Part of: Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

D. M. O'Brien
D. M. O'Brien
Affiliation:
Department of Mathematical Physics The University of AdelaideAdelaide, South Australia
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Abstract

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This note shows how the rate of decay of the singular values can be easily estimated for a wide class of integral operators on L2(Rn).

MSC classification

Secondary: 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 193 - 196
Copyright
Copyright © Australian Mathematical Society 1982

References

Sh. Birman, M. and Solomyak, M. Z. (1977), ‘Estimates of singular numbers of integral operators’, Russian Math. Surveys 32, 15–89.CrossRefGoogle Scholar
Gohberg, I. C. and Krein, M. G. (1969), ‘Introduction to the theory of linear non-selfadjoint operators’, Translations of Mathematical Monographs 18, (Amer. Math. Soc., Providence, Rhode Island).Google Scholar
Titchmarsh, E. C. (1958), Eigenfunction expansions associated with second order differential equations, part II (Oxford University Press, Oxford)Google Scholar