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

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

2010-08-09

arxiv.org/abs/1008.1526v2

J. Diff. Eq. 250, 3701-3739 (2011)

Mathematics

Spectral Theory

35 pages

Scientific paper

10.1016/j.jde.2010.10.026

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.

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