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Asymptotic Behaviour of Eigen-Values of Certain Integral Equations

Published online by Cambridge University Press:  20 January 2009

J. B. Reade
J. B. Reade
Affiliation:
The University of Manchester
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The integral equations we consider are

and

where 0 < α < 1. The asymptotic behaviour of the eigen-values of the latter equation is already known (see (1) and (4)). The former equation has been studied by many authors but as yet no explicit statement seems to have been made about the behaviour of its eigen-values.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 22 , Issue 2 , June 1979 , pp. 137 - 144
Copyright
Copyright © Edinburgh Mathematical Society 1979

References

REFERENCES

(1)Kac, M., Distribution of eigen-values of certain integral operators. Mich. Math. J. 3 (1955–6), 141–8.CrossRefGoogle Scholar
(2)Pietsch, A., Nuclear Locally Convex Spaces (Springer-Verlag, 1972).Google Scholar
(3)Polya, G., and Szego, G., Uber den transfiniten Durchmesser (Kapazitatskonstante) von ebenen und raumlichen Punktmengen, Crelle's Journal 165 (1931), 4–49.Google Scholar
(4)Rosenblatt, M., Some results on the asymptotic behaviour of eigenvalues for a class of integral equations with translation kernels, J. Math. Mech. 12 (1963), 619–628.Google Scholar