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On the location of the essential spectra and regularity fields of complex Sturm—Liouville operators

Published online by Cambridge University Press:  14 November 2011

David Race
David Race
Affiliation:
Department of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
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Synopsis

In this paper the Sturm-Liouville expression τy = −(py′)′ + qy, with complex-valued coefficients is considered, and a number of results concerning the location of the essential spectrum of associated operators are obtained. Some of these are extensions or generalizations of results due to Birman, and Glazman, whilst others are new. These lead to criteria for the non-emptiness of the regularity field of the corresponding minimal operator—a condition which is needed in the theory of J-selfadjoint extensions. A complete determination of the regularity field is made when the equation τy = λ0y has two linearly independent solutions in L2[a,∞) for some complex λ0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 85 , Issue 1-2 , 1980 , pp. 1 - 14
Copyright
Copyright © Royal Society of Edinburgh 1980

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