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The spectra of well-posed operators

Published online by Cambridge University Press:  14 November 2011

Sobhy El-sayed Ibrahim
Sobhy El-sayed Ibrahim
Affiliation:
Benha University, Faculty of Science, Department of Mathematics, Benha B 13518, Egypt
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Abstract

In this paper, the general ordinary quasidifferential expression M of nth order, with complex coefficients, and its formal adjoint M− are considered. It is shown in the case of two singular endpomts and when all solutions of the equation and the adjoint equation are in (the limit-circle case) that all well-posed extensions of the minimal operator T0(M) have resolvents which are Hilbert Schmidt integral operators and consequently have a wholly discrete spectrum. This implies that all the regularly solvable operators have all of the standard essential spectra to be empty. These results extend those for the formally symmetric expression M studied in [1] and [14], and also extend those proved in [8] for one singular endpoint.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 6 , 1995 , pp. 1331 - 1348
Copyright
Copyright © Royal Society of Edinburgh 1995

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