Skip to main content Accessibility help

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

  • C. A. Stuart (a1)


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.



Hide All
Browder, F. E., 1961. On the spectral theory of elliptic differential operators, Math. Annln, 142, 22139.
Chisholm, R. S. and Everitt, W. N., 1971. On bounded integral operators in the space of integrable-square functions, Proc. Roy. Soc. Edinb., 69A, 199204.
Dunford, N. and Schwartz, J. T., 1963. Linear Operators, Part II. New York: Interscience.
Kato, T., 1966. Perturbation Theory for Linear Operators. Berlin: Springer.
Naimark, M. A., 1968. Linear Differential Operators, Part II. London: Harrap.
Nussbaum, R. D., 1970. The radius of the essential spectrum, Duke Math. J., 37, 473478.
Stuart, C. A., 1973. Some bifurcation theory for K-set contractions, Proc. Lond. Math. Soc. (in press).
Yosida, K., 1966. Functional Analysis (1st Edn.). Berlin: Springer.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed