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Eigenvalues of positive integral operators with certain entire kernels

Published online by Cambridge University Press:  24 October 2008

G. Little
G. Little
Affiliation:
Department of Mathematics, University of Manchester
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Extract

Suppose that (an) (n ≥ 0) is a square-summable sequence of strictly positive real numbers; then the integral operator T on L2(− 1,1) given by

is compact and positive and, therefore, its eigenvalues can be arranged into a sequence λ0 ≥ λ1 ≥ λ2 ≥ … of non-negative real numbers which decreases to 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 3 , May 1986 , pp. 535 - 545
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1]Little, G.. Asymptotic estimates of the eigenvalues of certain positive Fredholm operators. Math. Proc. Cambridge Philos. Soc. 91 (1982), 267–284.CrossRefGoogle Scholar
[2]Halmos, P. R. and Sunder, V.S. Bounded Integral Operators on L2 spaces. Ergebnisee der Mathematik, 96 (Springer, 1978).CrossRefGoogle Scholar