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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.
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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.

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

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