On the Absolutely Continuous Spectrum of a Vector-Matrix Dirac System

Stephen L. Clark

doi:10.1017/S0308210500028456

On the Absolutely Continuous Spectrum of a Vector-Matrix Dirac System

Stephen L. Clark

Mathematics and Statistics

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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.

Original language	American English
Journal	Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume	124
DOIs	https://doi.org/10.1017/S0308210500028456
State	Published - Mar 1 1994

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Mathematics
Statistics and Probability

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https://doi.org/10.1017/S0308210500028456

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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.",

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AB - 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.

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JO - Proceedings of the Royal Society of Edinburgh: Section A Mathematics

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On the Absolutely Continuous Spectrum of a Vector-Matrix Dirac System

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