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On the unboundedness below of the Sturm—Liouville operator

Published online by Cambridge University Press:  14 November 2011

Manfred Möller
Manfred Möller
Affiliation:
Department of Mathematics. University of the Witwatersrand, Johannesburg. WITS 2050., South Africa
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Abstract

We show that if the leading coefficient p in a Sturm-Liouville expression is negative on a set E with positive Lebesgue measure, then the minimal operator (and hence any self-adjoint realization of the Sturm-Liouville expression) is not bounded below. The case when E contains an interval follows from standard methods but these methods fail when E contains no interval, e.g. when E is a Cantor-like set. This is the case considered here.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 129 , Issue 5 , 1999 , pp. 1011 - 1015
Copyright
Copyright © Royal Society of Edinburgh 1999

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