Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T09:43:40.117Z Has data issue: false hasContentIssue false
  • English
  • Français

A fourth order limit-3 expression with nonempty essential spectrum

Published online by Cambridge University Press:  14 November 2011

Bernd Schultze
Bernd Schultze
Affiliation:
Fachbereich 6, Mathematik, Universität GH Essen, Universitätsstr 3, 4300 Essen, F.R.G.
Get access Rights & Permissions [Opens in a new window]

Synopsis

It is shown that even in the fourth order case there exist real symmetric ordinary differential expressions with nonempty essential spectrum which are not in the limit-point case.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 233 - 235
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

1Goldberg, S.. Unbounded linear operators (New York: McGraw-Hill, 1966).Google Scholar
2Grudniewicz, C. G. M.. Asymptotic methods for fourth-order differential equations. Proc. Roy. Soc. Edinburgh Sect. A 87 (1980), 53–63.CrossRefGoogle Scholar
3Kauffman, R. M.. On the limit-n classification of ordinary differential operators with positive coefficients. Proc. London Math. Soc. (3) 35 (1977), 496–526.CrossRefGoogle Scholar
4Rota, G. C., Extension theory of differential operators. Comm. Pure Appl. Math. 11 (1958), 23–65.CrossRefGoogle Scholar
5Schultze, B.. A construction of symmetric differential expressions with nonempty essential spectrum. Proc. Roy. Soc. Edinburgh Sect. A 105 (1987), 193–194.CrossRefGoogle Scholar
6Schuitze, B.. Odd-order differential expressions with positive supporting coefficients. Proc. Roy. Soc. Edinburgh Sect. A 105 (1987), 167–192.CrossRefGoogle Scholar
7Schultze, B.. On the essential spectrum of linear ordinary differential expressions (to appear).Google Scholar