Title: Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory: Advances and Applications)
Publisher: Birkh�user Basel
Publication Date: 1997
Language: English
ISBN 10: 3764357630
ISBN 13: 9783764357634
Binding: Hardcover
Condition: New

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Synopsis

Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares. This book develops the realization theory of such functions as characteristic functions of coisometric, isometric, and unitary colligations whose state spaces are reproduced kernal Pontryagin spaces. This provides a modern system theory setting for the relationship between invariant subspaces and factorization, operator models, Krein-Langer factorizations, and other topics. This text is intended for students and researchers in mathematics and engineering. An introductory chapter contains background material, including reproducing kernal Pontryagin spaces, complementary spaces in the sense of de Branges, and a result on defining operators as closures of linear relations. The presentation is such that the indefinite case is handled parallel to the definite case.

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