Schur Functions, Operator Colligations and Reproducing Kernel Pontryagin Spaces

By:

Daniel Alpay

Format:

Hardback

Series:

Operator Theory: Advances and Applications

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Description

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.

Release date Australia

May 31st, 1997

Author

Daniel Alpay

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational
Undergraduate

Country of Publication

Switzerland

Imprint

Birkhauser Verlag AG

Pages

224

Publisher

Birkhauser Verlag AG

Series

Operator Theory: Advances and Applications

ISBN-13

9783764357634

Product ID

13188208

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