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

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 $xq(x)\in L^1(0,1)$. 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.

35 pages

References in corpus (2)

• Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators
• Regular singular Sturm-Liouville operators and their zeta-determinants

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