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 (1)

• Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators

Cited by in corpus (5)

• Weyl-Titchmarsh Theory for Sturm-Liouville Operators with Distributional Potentials
• On the isospectral problem of the dispersionless Camassa-Holm equation
• On Spectral Deformations and Singular Weyl Functions for One-Dimensional Dirac Operators
• On domain properties of Bessel-type operators
• The conservative Camassa-Holm flow with step-like irregular initial data