On linear fractional transformations associated with generalized J-inner matrix functions

Details On linear fractional transformations associated with generalized J-inner matrix functions On linear fractional transformations associated with generalized J-inner matrix functions

2009-01-01

arxiv.org/abs/0901.0193v2

Integr. Equ. Oper.Th., 65 (2009), 1-50

Mathematics

Functional Analysis

41 pages

Scientific paper

10.1007/s00020-009-1709-7

In this paper we study generalized J-inner matrix valued functions which appear as resolvent matrices in various indefinite interpolation problems. Reproducing kernel indefinite inner product spaces associated with a generalized J-inner matrix valued function W are studied and intensively used in the description of the range of the linear fractional transformation associated with W and applied to the Schur class. For a subclass of generalized J-inner matrix valued function W the notion of associated pair is introduced and factorization formulas for W are found.

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