Abstract
SynopsisThe theory of subordinacy is extended to all one-dimensional Schrödinger operatorsfor which the corresponding differential expressionL= –d2/(dr2) +V(r) is in the limit point case at both ends of an interval (a,b), withV(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 ofLu = xu, x εℝ, asr→aandr→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.
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