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M-function behaviour for a periodic Dirac system

Published online by Cambridge University Press:  14 November 2011

Dominic P. Clemence
Dominic P. Clemence
Affiliation:
Department of Mathematics, University of Zimbabwe, P.O. Box MP 167, Mount Pleasant, Harare, Zimbabwe
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Abstract

For a 2 × 2 periodic system with a perturbation P whose first moment is finite, Jy′ = [λI + R(x) + P(x)]y, we study the behaviour of the Titchmarsh–Weyl m(λ)-coefficient at the spectral gap endpoints. Assuming gap nondegeneracy, our main result is that as λ → λ0, (λ − λ0)½(m(λ) → c ≠ 0 if and only if λ0 is a φ-half-bound state, which follows from an analysis of Jost-type functions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 1 , 1994 , pp. 149 - 159
Copyright
Copyright © Royal Society of Edinburgh 1994

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References

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