TY - BOOK

T1 - Schur functions, operator colligations, and reproducing kernel Pontryagin spaces

AU - Alpay, Daniel

AU - Dijksma, Aad

AU - Rovnyak, James

AU - de Snoo, hendrik

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

KW - Operator theory

KW - differential equation

KW - function theory

KW - linear system theory

KW - mathematics

KW - system theory

U2 - https://doi.org/10.1007/978-3-0348-8908-7

DO - https://doi.org/10.1007/978-3-0348-8908-7

M3 - Book

SN - 3764357630

T3 - Operator theory, advances and applications

BT - Schur functions, operator colligations, and reproducing kernel Pontryagin spaces

PB - Birkhauser

CY - Basel, Switzerland

ER -