1 edition of **Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces** found in the catalog.

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- 5 Currently reading

Published
**1997**
by Birkhäuser Basel, Imprint: Birkhäuser in Basel
.

Written in 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.

**Edition Notes**

Statement | by Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik Snoo |

Series | Operator Theory Advances and Applications -- 96, Operator theory, advances and applications -- 96. |

Contributions | Dijksma, Aad, Rovnyak, James, Snoo, Hendrik |

The Physical Object | |
---|---|

Format | [electronic resource] / |

Pagination | 1 online resource. |

ID Numbers | |

Open Library | OL27086526M |

ISBN 10 | 3034889089 |

ISBN 10 | 9783034889087 |

OCLC/WorldCa | 840291193 |

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces, Operator Theory: Advances and Applications, vol. 96 by Daniel Alpay, Aad Dijksma, James Rovnayk, Hendrik de Snoo (pp. ). Explore books by Daniel Alpay with our selection at Click and Collect from your local Waterstones or get FREE UK delivery on orders over £

Operator Theory, Advances and Applications(1st Edition) Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces No. 96 by Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik De Snoo Hardcover, Pages, Published by Birkhauser ISBN , ISBN: Discount prices on books by James Rovnyak, including titles like Square Summable Power Series (Dover Books on Mathematics). Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory. Author: Daniel Alpay, Aad Dijksma, James Rovnyak. Paperback Oct

Stephen L. Adler, Quaternionic quantum mechanics and quantum fields, International Series of Monographs on Physics, vol. 88, The Clarendon Press, Oxford University Press, New York, MR Daniel Alpay, The Schur algorithm, reproducing kernel spaces and system theory, SMF/AMS Texts and Monographs, vol. 5, American Mathematical Society, Providence, RI; Cited by: Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik S V De Snoo.

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Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces. Authors: Alpay, D., Dijksma, A., Rovnyak, J., Snoo, Schur Functions. de Free Preview. 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. Get this from a library.

Schur functions, operator colligations, and reproducing kernel Pontryagin spaces. [Daniel Alpay;] -- 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. Additional Physical Format: Online version: Schur functions, operator colligations, and reproducing kernel Pontryagin spaces. Operator Colligations ; Boston: Birkhäuser Verlag, © After a review of reproducing kernel Pontryagin spaces, it is shown in § that a holomorphic kernel has the same number of negative squares for every region of analyticity.

Background on colligations and their characteristic functions is presented in §Author: Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik de Snoo.

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik de Snoo (auth.) Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares.

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces, Daniel Alpay, Aad Dijksma, James Rovnayk, Hendrik de Snoo, Operator Theory: Advances and Applications, vol.

96, Birkhâuser Verlag, Basel - Boston - Berlin,+xi pag., ISBNISBN Keywords: Schur functions, reproducing kernel. generalized Schur functions and associated colligations and reproducing kernel Pontryagin spaces. Mathematics Subject Classi cation.

Primary 46C20, 46E Secondary 47B Key words and phrases. Pontryagin space, reproducing kernel, negative squares, Schur class, contraction operator. Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces av Daniel Alpay Generalized Schur functions are scalar- or operator-valued holomorphic functions such that certain associated kernels have a finite number of negative squares.

Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces (Operator Theory: Advances and Applications) by Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik De Snoo ISBN ().

On Some Operator Colligations and Associated Reproducing Kernel Pontryagin Spaces D. Alpay and V. Bolotnikov Department of Mathematics, Ben-Gurion University of the Negev, POBBeer-Sheva, Israel A.

Dijksma and H. de Snoo Vakgroep Wiskunde, Rijksuniversiteit Groningen, PostbusAV Grongingen, The Netherlands Received November. The main theme of the first half of this paper rests upon the fact that there is a reproducing kernel Hilbert space of vector valued functions B (X) associated with each suitably restricted matrix.

In this book, Alpay looks at matrix-valued Schur functions and their applications from the unifying point of view of spaces with reproducing kernels. This approach is used here to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators.5/5(1).

[B1] D. Alpay, A. Dijksma, J. Rovnyak and H. de Snoo. Schur functions, operator colligations and reproducing kernel Pontryagin spaces. Volume 96 in the series Operator Theory: Advances and Applications (). Articles [] D. Alpay and A.

Pinhas. Stochastic Wiener filter in. The theory of reproducing kernel Pontryagin spaces is sur- veyed. A new proof is given of an abstract theorem that constructs contrac- tion operators on Pontryagin spaces from densely dened relations.

Email your librarian or administrator to recommend adding this book to your organisation's collection. The Theory of H(b) Spaces. and de Snoo, H. Schur functions, operator colligations, and reproducing kernel Pontryagin spaces, vol.

96 of Operator Theory: Advances and Applications. Birkhäuser, Cited by: Using reproducing kernel Hilbert spaces methods we develop a Schur-type algorithm for a subclass of the functions analytic and contractive in the ball. We also consider the Nevanlinna–Pick interpolation problem in that by: Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces $ CAD SKU: Add to basket; One-Dimensional Linear Singular Integral Equations Vol.

II $ CAD SKU: Add to basket; Stochastic Analysis and Related Topics VI: Proceedings of the Sixth Oslo-Silivri Workshop, Geilo $ CAD SKU: There is a one-to-one correspondance between such functions and reproducing kemel Pontryagin spaces.

We refer the reader to [10] for the Hilbert space case and to [22, 21, 5] for the case of Pontryagin spaces. Rovnyak, H. de Snoo, Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin spaces, Operator Theory: Advances and Cited by: 3.

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces (Cambridge Studies in Advanced Mathematics) Cholesky and Schur operations on kernels, and vector-valued spaces. Self-contained and accessibly written, with exercises at the end of each chapter, this unrivalled treatment of the topic serves as an ideal introduction for Cited by:.

D. Alpay et al. / Linear Algebra and its Applications () – 2. Pick’s theorem and some preliminaries A function S: BN→ Cp×q is called a Schur multiplier if the operator MS of multiplication by Son the left given by F → SF is a contraction from (H(BN))qinto (H(BN))= 1, Schur multipliers are exactly the Cp×q-valued functions analytic and .Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces.

Birkhäuser Basel. Daniel Alpay, Aad Dijksma, James Rovnyak, Hendrik de Snoo (auth.) A search query can be a title of the book, a name of the author, ISBN or anything else. Read more about ZAlerts.An H(b) space is defined as a collection of analytic functions that are in the image of an operator.

The theory of H(b) spaces bridges two classical subjects, complex analysis and operator theory, which makes it both appealing and by: