Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-17T23:17:25.856Z Has data issue: false hasContentIssue false

A construction of symmetric differential expressions with non-empty essential spectrum*

Published online by Cambridge University Press:  14 November 2011

Bernd Schultze
Affiliation:
Department of Mathematics, Universität-GHS Essen, Postfach 103764, 4300 Essen 1, West Germany

Synopsis

A simple method is given for the construction of real symmetric differential expressions that are not in the limit-point case but have the real half-line as essential spectrum.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1987

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Dunford, N. and Schwartz, J. T.. Linear operators, part II, (New York: Interscience Publishers, 1963).Google Scholar
2Kauffman, R. M., Read, T. T. and Zettl, A.. The deficiency index problem for powers of ordinary differential expressions. Lecture Notes in Mathematics 621 (Berlin: Springer, 1977).Google Scholar
3Kogan, V. I. and Rofe-Beketov, F. S.. On the question of deficiency indices of differential operators with complex coefficients. Proc. Roy. Soc. Edinburgh Sect. A 72 (1973/1974), 281298.CrossRefGoogle Scholar
4McLeod, J. B.. The number of square-integrable solutions of ordinary differential equations. Quart. J. Math. Oxford Ser. (2) 17 (1966), 285290.CrossRefGoogle Scholar
5Naimark, M. A.. Linear differential operators, Part II (Moscow: GITTL, 1954). English translation (New York: Ungar, 1968).Google Scholar
6Rota, G. C.. Extension theory of differential operators. Comm. Pure Appl. Math. 11 (1958), 2365.CrossRefGoogle Scholar
7Schultze, B.. Odd-order differential expressions with positive supporting coefficients. Proc. Roy. Soc. Edinburgh 105A (1987), 167192.CrossRefGoogle Scholar