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On the Titchmarsh-Weyl M(λ)-coefficient and spectral density for a Dirac system

Published online by Cambridge University Press:  14 November 2011

Dominic P. Clemence
Dominic P. Clemence
Affiliation:
Department of Mathematics, Virginia Polytechnic Instituteand State University, Blacksburg, Virginia 24061, U.S.A.
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Synopsis

For a Dirac system on the line, we study the Jost solutions and the existence of half-bound states. A characterisation of this phenomenon is given in terms of the M(λ)-function, which supplements a well-known spectral characterisation for the system. As a corollary, we deduce the spectral density behaviour at the spectral gap endpoints, which is shown to depend on the possible existence of half-bound states.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 259 - 277
Copyright
Copyright © Royal Society of Edinburgh 1990

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