J Contractive Matrix Functions Reproducing Kernel Hilbert Spaces And Interpolation

Author : Harry Dym
Publisher : American Mathematical Soc.
ISBN 13 : 0821807226
Total Pages : 159 pages
Book Rating : 4.24/5 ( download)

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Download or read book $J$ Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces and Interpolation written by Harry Dym and published by American Mathematical Soc.. This book was released on 1989 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an introduction to the theory and applications of $J$ inner matrices. This book discusses matrix interpolation problems including two-sided tangential problems of both the Nevanlinna-Pick type and the Caratheodory-Fejer type, as well as mixtures of these.

Author : Damir Z. Arov
Publisher : Cambridge University Press
ISBN 13 : 0521883008
Total Pages : 576 pages
Book Rating : 4.09/5 ( download)

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Download or read book J-Contractive Matrix Valued Functions and Related Topics written by Damir Z. Arov and published by Cambridge University Press. This book was released on 2008-11-06 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to the theory of J-contractive and J-inner matrix valued functions with respect to the open upper half-plane and a number of applications of this theory. It will be of particular interest to those with an interest in operator theory and matrix analysis.

Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3034889089
Total Pages : 244 pages
Book Rating : 4.87/5 ( download)

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Download or read book Schur Functions, Operator Colligations, and Reproducing Kernel Pontryagin Spaces written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Daniel Alpay
Publisher : Springer Science & Business Media
ISBN 13 : 3764375477
Total Pages : 304 pages
Book Rating : 4.78/5 ( download)

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Download or read book Interpolation, Schur Functions and Moment Problems written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2006-06-22 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schur analysis originated with an 1917 article which associated to a function, which is analytic and contractive in the open unit disk, a sequence, finite or infinite, of numbers in the open unit disk, called Schur coefficients, often named reflection coefficients in signal processing. This volume comprises seven essays dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.

Author : H. Bart
Publisher : Birkhäuser
ISBN 13 : 3034856725
Total Pages : 383 pages
Book Rating : 4.20/5 ( download)

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Download or read book Topics in Matrix and Operator Theory written by H. Bart and published by Birkhäuser. This book was released on 2013-11-22 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Joseph A. Ball
Publisher : Birkhäuser
ISBN 13 : 3034878818
Total Pages : 604 pages
Book Rating : 4.14/5 ( download)

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Download or read book Current Trends in Operator Theory and its Applications written by Joseph A. Ball and published by Birkhäuser. This book was released on 2012-12-06 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many developments on the cutting edge of research in operator theory and its applications are reflected in this collection of original and review articles. Particular emphasis lies on highlighting the interplay between operator theory and applications from other areas, such as multi-dimensional systems and function theory of several complex variables, distributed parameter systems and control theory, mathematical physics, wavelets, and numerical analysis.

Author : Foias
Publisher : Birkhäuser
ISBN 13 : 3034877129
Total Pages : 647 pages
Book Rating : 4.21/5 ( download)

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Download or read book The Commutant Lifting Approach to Interpolation Problems written by Foias and published by Birkhäuser. This book was released on 2013-11-11 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical H interpolation theory was conceived at the beginning of the century by C. Caratheodory, L. Fejer and I. Schur. The basic method, due to Schur, in solving these problems consists in applying the Mobius transform to peel off the data. In 1967, D. Sarason encompassed these classical interpolation problems in a representation theorem of operators commuting with special contractions. Shortly after that, in 1968, B. Sz. Nagy and C. Foias obtained a purely geometrical extension of Sarason's results. Actually, their result states that operators intertwining restrictions of co-isometries can be extended, by preserving their norm, to operators intertwining these co-isometries; starring with R. G. Douglas, P. S. Muhly and C. Pearcy, this is referred to as the commutant lifting theorem. In 1957, Z. Nehari considered an L interpolation problern which in turn encompassed the same classical interpolation problems, as well as the computation of the distance of a function f in L to H . At about the sametime as Sarason's work, V. M."

Author : Saburou Saitoh
Publisher : CRC Press
ISBN 13 : 1000115240
Total Pages : 289 pages
Book Rating : 4.46/5 ( download)

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Download or read book Integral Transforms, Reproducing Kernels and Their Applications written by Saburou Saitoh and published by CRC Press. This book was released on 2020-11-25 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.

Author : G. Arsene
Publisher : Birkhäuser
ISBN 13 : 303487250X
Total Pages : 344 pages
Book Rating : 4.08/5 ( download)

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Download or read book Linear Operators in Function Spaces written by G. Arsene and published by Birkhäuser. This book was released on 2012-12-06 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Operator Theory conferences, organized by the Department of Mathematics of INCREST and the Department of Mathematics of the University of Timi~oara, are conceived as a means to promote cooperation and exchange of information between specialists in all areas of operator theory. This book comprises carefully selected papers on theory of linear operators and related fields. Original results of new research in fast developing areas are included. Several contributed papers focus on the action of linear operators in various function spaces. Recent advances in spectral theory and related topics, operators in indefinite metric spaces, dual algebras and the invariant subspace problem, operator algebras and group representations as well as applications to mathematical physics are presented. The research contacts of the Department of :viathematics of INCREST with the National Committee for Science and Technology of Romania provided means for developing the research activity in mathematics; they represent the generous framework of these meetings too. It is our pleasure to acknowledge the financial support of UNESCO which also contributed to the success of this meeting. We are indebted to Professor Israel Gohberg for including these Proceedings in the OT Series and for valuable advice in the editing process. Birkhauser Verlag was very cooperative in publishing this volume. Camelia Minculescu, Iren Nemethi and Rodica Stoenescu dealt with the difficult task of typing the whole manuscript using a Rank Xerox 860 word processor; we thank them for this exellent job.

Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3319688499
Total Pages : 495 pages
Book Rating : 4.97/5 ( download)

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Download or read book Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations written by Daniel Alpay and published by Birkhäuser. This book was released on 2018-01-30 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, which is dedicated to Heinz Langer, includes biographical material and carefully selected papers. Heinz Langer has made fundamental contributions to operator theory. In particular, he has studied the domains of operator pencils and nonlinear eigenvalue problems, the theory of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and applications to mathematical physics. His works include studies on and applications of Schur analysis in the indefinite setting, where the factorization theorems put forward by Krein and Langer for generalized Schur functions, and by Dijksma-Langer-Luger-Shondin, play a key role. The contributions in this volume reflect Heinz Langer’s chief research interests and will appeal to a broad readership whose work involves operator theory.