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On the absolutely continuous spectrum of a vector-matrix Dirac system

Published online by Cambridge University Press:  14 November 2011

Stephen L. Clark
Stephen L. Clark
Affiliation:
Department of Mathematics and Statistics, University of Missouri-Rolla, Rolla, Missouri 65401, U.S.A.
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Abstract

A Dirac system is considered which has a matrix-valued long-range, short-range and oscillatory potentials. The system has one singular endpoint at infinity. Additional conditions on the potential are given which guarantee particular asymptotic behaviour of an energy functional associated with a certain set of solutions. This asymptotic behaviour guarantees the existence of a purely absolutely continuous spectrum outside a gap containing the origin.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 2 , 1994 , pp. 253 - 262
Copyright
Copyright © Royal Society of Edinburgh 1994

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