On the singular Weyl–Titchmarsh function of perturbed spherical Schrödinger operators

We investigate the singular Weyl–Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q ( x ) satisfies x q ( x ) ∈ L 1 ( 0 , 1 ) . We show existence plus detailed properties of a fundamental system of solution...

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Bibliographic Details
Published in:	Journal of Differential Equations Vol. 250; no. 9; pp. 3701 - 3739
Main Authors:	Kostenko, Aleksey, Teschl, Gerald
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-05-2011
Subjects:	Bessel operators Schrödinger operators Weyl–Titchmarsh theory secondary Schrödinger operators Bessel operators Weyl–Titchmarsh theory primary
Online Access:	Get full text
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Summary:	We investigate the singular Weyl–Titchmarsh m-function of perturbed spherical Schrödinger operators (also known as Bessel operators) under the assumption that the perturbation q ( x ) satisfies x q ( x ) ∈ L 1 ( 0 , 1 ) . We show existence plus detailed properties of a fundamental system of solutions which are entire with respect to the energy parameter. Based on this we show that the singular m-function belongs to the generalized Nevanlinna class and connect our results with the theory of super singular perturbations.
ISSN:	0022-0396 1090-2732
DOI:	10.1016/j.jde.2010.10.026