10-122 Aleksey Kostenko and Gerald Teschl

On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators (97K, LaTeX2e) Aug 9, 10

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Abstract. We investigate the singular Weyl--Titchmarsh $m$-function of perturbed spherical Schr\"odinger 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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