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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

Dominic P. Clemence
Dominic P. Clemence*
Affiliation:
Department of Mathematics, NCA&T State University, Greensboro, North Carolina 27411, U.S.A., e-mail: [email protected]
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Abstract

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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.

Keywords

34L0534B2034B24
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 4 , 01 December 1997 , pp. 416 - 421
Copyright
Copyright © Canadian Mathematical Society 1997

References

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