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Levinson's theorem and Titchmarsh-Weyl m(λ) theory for Dirac systems*

Published online by Cambridge University Press:  14 November 2011

D. B. Hinton ,
M. Klaus  and
J. K. Shaw
D. B. Hinton
Affiliation:
Mathematics Department, University of Tennessee, Knoxville, TN 37996, U.S.A.
M. Klaus
Affiliation:
Mathematics Department, Virginia Tech, Blacksburg, VA 24061, U.S.A.
J. K. Shaw
Affiliation:
Mathematics Department, Virginia Tech, Blacksburg, VA 24061, U.S.A.
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Synopsis

A Levinson theorem is proved for a Dirac system with one singular endpoint. The number ofbound state is expressed in terms of the change in asymptotic phase of an appropriate solution and in terms of factors whose values depend on the presence of half-bound states. The behaviour of the asymptotic phase is used to determine the asymptotic behaviour of the Titchmarsh-Weyl m-function.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 1-2 , 1988 , pp. 173 - 186
Copyright
Copyright © Royal Society of Edinburgh 1988

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