Levinson's theorem and Titchmarsh-Weyl m(λ) theory for Dirac systems*
- 1 January 1988
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 109 (1-2) , 173-186
- https://doi.org/10.1017/s0308210500026743
Abstract
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.Keywords
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