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15.—The Measure of Non-compactness of Some Linear Integral Operators

Published online by Cambridge University Press:  14 February 2012

C. A. Stuart
C. A. Stuart
Affiliation:
University of Sussex.
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Synopsis

The measure of non-compactness of linear integral operators on the half-line [0, ∞) of a special type is studied. In particular, a necessary and sufficient condition is established for an operator of this type to define a compact operator from L2(0, ∞) into itself. These results are then used to discuss the spectrum of second-order differential operators. A necessary and sufficient condition for the spectrum to be discrete is established together with estimates for the distance of a point in the resolvent set from the essential spectrum.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 71 , Issue 2 , 1973 , pp. 167 - 179
Copyright
Copyright © Royal Society of Edinburgh 1973

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References

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