Hostname: page-component-6bb9c88b65-bcq64 Total loading time: 0 Render date: 2025-07-21T05:54:36.643Z Has data issue: false hasContentIssue false
  • English
  • Français

A class of symmetric ordinary differential operators whose deficiency numbers differ by an integer†

Published online by Cambridge University Press:  14 November 2011

Richard C. Gilbert
Richard C. Gilbert
Affiliation:
California State University, Fullerton, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

Formulas are determined for the deficiency numbers of a formally symmetric ordinary differential operator with complex coefficients which have asymptotic expansions of a prescribed type on a half-axis. An implication of these formulas is that for any given positive integer there exists a formally symmetric ordinary differential operator whose deficiency numbers differ by that positive integer.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 117 - 134
Copyright
Copyright © Royal Society of Edinburgh 1978

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.)

Article purchase

Temporarily unavailable

References

1Atkinson, F. V.. Discrete and continuous boundary problems (New York: Academic, 1964).Google Scholar
2Bellman, R.. Stability theory of differential equations (New York: McGraw-Hill, 1953).Google Scholar
3Devinatz, A.. The deficiency index of ordinary self-adjoint differential operators. Pacific J. Math. 16 (1966), 243–257.CrossRefGoogle Scholar
4Dunford, N. and Schwartz, J. T.. Linear operators, II (New York: Interscience, 1963).Google Scholar
5Everitt, W. N.. Integrable-square solutions of ordinary differential operators. Quart. J. Math. Oxford Ser. 10 (1959), 145–155.CrossRefGoogle Scholar
6Everitt, W. N.. Singular differential equations I: the even order case. Math. Ann. 156 (1964), 9–24.CrossRefGoogle Scholar
7Fedorjuk, M. V.. Asymptotic methods in the theory of one-dimensional singular differential operators. Trans. Moscow Math. Soc. 15 (1966), 333–386.Google Scholar
8Gilbert, R. C.. Asymptotic formulas for solutions of a singular linear ordinary differential equation. Proc. Roy. Soc. Edinburgh. Sect. A 81 (1978), 57–70.CrossRefGoogle Scholar
9Glazman, I. M.. On the theory of singular differential operators. Uspehi Mat. Nauk. 5 (1950), 102–135.Google Scholar
10Kogan, V. L. and Rofe-Beketov, F. S.. On the question of the deficiency indices of differential operators with complex coefficients. Proc. Roy. Soc. Edinburgh. Sect. A 72 (1975), 281–198.CrossRefGoogle Scholar
11Kogan, V. I. and Rofe-Beketov, F. S.. On square-integrable solutions of symmetric systems of differential equations of arbitrary order. Proc. Roy. Soc. Edinburgh. Sect. A 74 (1976), 5–40.CrossRefGoogle Scholar