Journal of Operator Theory

Volume 42, Issue 1, Summer 1999 pp. 145-188.

Interpolation in generalized Nevanlinna and Stieltjes classes

Authors: Arthur Amirshadyan (1), and Vladimir Derkach (2)
Author institution: (1) Department of Mathematics, State University, Universiteskaya str. 24, Donetsk 340055, Ukraine
(2) Department of Mathematics, State University, Universiteskaya str. 24, Donetsk 340055, Ukraine

Summary: A two-sided indefinite interpolation problem in the class of generalized Nevanlinna pairs is considered. In the case where the Pick matrix is nondegenerate a solvability criterion for the problem is given. All solutions of the problem are described as a fractional linear transformations of a parameter from a subclass of the Nevanlinna class. The nondegenerate interpolation problem in the generalized Stieltjes class has the same solution matrix and the parameter ranges over a subclass of the Stieltjes class. Sufficient conditions for the problems to have no excluded parameters are given in terms of the reproducing kernel matrices.

Keywords: Interpolation, Nevanlinna pair, Pontryagin space, symmetric operator, selfadjoint extension, generalized resolvent, resolvent matrix

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