On the reproducing kernel of a Pontryagin space of vector valued polynomials

We give necessary and sufficient conditions under which the reproducing kernel of a Pontryagin space of $d \times 1$ vector polynomials is determined by a generalized Nevanlinna pair of $d \times d$ matrix polynomials.Comment: 33 page

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

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.Comment: 35 page

Some extensions of Loewner's theory of monotone operator functions

Several extensions of Loewner's theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class, The theory of monotone operator functions is generalized from scalar- to matrix-valued functions of an operator argument. A notion of kappa-monotonicity is introduced and characterized in terms of classical Nevanlinna functions with removable singularities on a real interval. Corresponding results for Stieltjes functions are presented. (C) 2002 Elsevier Science (USA).</p

Some Extensions of Loewner\u27s Theory of Monotone Operator Functions

Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalar- to matrix-valued functions of an operator argument. A notion of -monotonicity is introduced and characterized in terms of classical Nevanlinna functions with removable singularities on a real interval. Corresponding results for Stieltjes functions are presented