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On the Singular Behaviour of the Titchmarsh-Weyl m-Function for the Perturbed Hill’s Equation on the Line
Published online by Cambridge University Press: 20 November 2018
Abstract
For the perturbed Hill’s equation on the line,
we study the behaviour of the matrix m-function at the spectral gap endpoints. In particular, we extend the result of Hinton, Klaus and Shaw that En, a gap endpoint, is a half-bound state (HBS) if and only if (E − En)½m(E) approaches a nonzero constant as E → En, to the present case.
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- Research Article
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- Copyright © Canadian Mathematical Society 1997