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Operator Theory: Advances and Applications

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces

Authors: Alpay, D., Dijksma, A., Rovnyak, J., Snoo, H. de

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About this book

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.

Table of contents (4 chapters)

Table of contents (4 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-3-0348-8908-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA in USD
  • ISBN 978-3-0348-9823-2
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
96
Copyright
1997
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-8908-7
DOI
10.1007/978-3-0348-8908-7
Softcover ISBN
978-3-0348-9823-2
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XI, 232
Topics

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