On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators

Aleksey Kostenko; Gerald Teschl

doi:10.1016/j.jde.2010.10.026

On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators

Spectral Theory 2011-03-01 v2 Mathematical Physics Classical Analysis and ODEs math.MP

Authors: Aleksey Kostenko , Gerald Teschl

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Abstract

We investigate the singular Weyl-Titchmarsh m-function of perturbed spherical Schroedinger operators (also known as Bessel operators) under the assumption that the perturbation $q(x)$ satisfies $x q(x) \in L^1(0,1)$ . 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.

Keywords

schrödinger operators operator theory special functions

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@article{arxiv.1008.1526,
  title  = {On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators},
  author = {Aleksey Kostenko and Gerald Teschl},
  journal= {arXiv preprint arXiv:1008.1526},
  year   = {2011}
}

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35 pages

On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators

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