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

Daniel Alpay/ Aad Dijksma/ James Rovnyak/ Hendrik de Snoo

ISBN 10: 3764357630 / ISBN 13: 9783764357634

Published by Birkhäuser Basel, 1998

About this Item

224 pages. 9.61x6.69x0.63 inches. In Stock. Seller Inventory # x-3764357630

Bibliographic Details

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

Publisher: Birkhäuser Basel

Publication Date: 1998

Binding: Hardcover

Condition: Brand 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.