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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

Dijksma, Aad
Rovnyak, James
Alpay, Daniel

Paperback

Series: Operator Theory: Advances and Applications, Book 96

Technology & EngineeringCalculusGeneral Mathematics

ISBN10: 3034898231
ISBN13: 9783034898232
Publisher: Springer Nature
Published: Oct 16 2012
Pages: 232
Weight: 0.90
Height: 0.53 Width: 6.69 Depth: 9.61
Language: English
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.

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