J. Differential Equations 250, 3701-3739 (2011) [DOI: 10.1016/j.jde.2010.10.026]

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

Aleksey Kostenko and Gerald Teschl

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) ∈ L1(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.

MSC2000: Primary 34B20, 34L40; Secondary 34B30, 34L05
Keywords: Schrödinger operators, Bessel operators, Weyl-Titchmarsh theory

TeX file (100K) or pdf file (474K)