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On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints

Published online by Cambridge University Press:  14 November 2011

D. J. Gilbert
D. J. Gilbert
Affiliation:
Department of Applied Mathematics, University of Hull, Hull HU6 7RX, U.K.
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Synopsis

The theory of subordinacy is extended to all one-dimensional Schrödinger operatorsfor which the corresponding differential expression L = – d2/(dr2) + V(r) is in the limit point case at both ends of an interval (a, b), with V(r) locally integrable. This enables a detailed classification of the absolutely continuous and singular spectra to be established in terms of the relative asymptotic behaviour of solutions of Lu = xu, x εℝ, as r→a and r→b. The result provides a rigorous but straightforward method of direct spectral analysis which has very general application, and somefurther properties of the spectrum are deduced from the underlying theory.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 112 , Issue 3-4 , 1989 , pp. 213 - 229
Copyright
Copyright © Royal Society of Edinburgh 1989

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