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On the essential spectra of linear 2nth order differential operators with complex coefficients

Published online by Cambridge University Press:  14 November 2011

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

In this paper, a formally J-symmetric, linear differential expression of 2nth order, with complex-valued coefficients, is considered. A number of results concerning the location of the essential spectrum of associated operators are obtained. These are extensions of earlier work dealing with complex Strum-Liouville operators, and include results which, in the real case, are due to Birman, Glazman and others. They 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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 65 - 75
Copyright
Copyright © Royal Society of Edinburgh 1982

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