Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory: Advances and Applications)

Daniel Alpay

ISBN 10: 3034898231 / ISBN 13: 9783034898232

Published by Springer 1997-07-15, 1997

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Seller Inventory # 6666-IUK-9783034898232

Bibliographic Details

Title: Schur Functions, Operator Colligations, and ...

Publisher: Springer 1997-07-15

Publication Date: 1997

Binding: Paperback

Condition: New

About this title

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 reproducing kernel 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. The book is intended for students and researchers in mathematics and engineering. An introductory chapter supplies background material, including reproducing kernel Pontryagin spaces, complementary spaces in the sense of de Branges, and a key result on defining operators as closures of linear relations. The presentation is self-contained and streamlined so that the indefinite case is handled completely parallel to the definite case.