The Commutant Lifting Approach To Interpolation Problems

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The Commutant Lifting Approach to Interpolation Problems

Author : Foias
Publisher : Birkhäuser
ISBN 13 : 3034877129
Total Pages : 632 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis The Commutant Lifting Approach to Interpolation Problems by : Foias

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 632 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."

Metric Constrained Interpolation, Commutant Lifting and Systems

Author : C. Foias
Publisher : Birkhäuser
ISBN 13 : 3034887914
Total Pages : 587 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Metric Constrained Interpolation, Commutant Lifting and Systems by : C. Foias

Download or read book Metric Constrained Interpolation, Commutant Lifting and Systems written by C. Foias and published by Birkhäuser. This book was released on 2012-12-06 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified approach for solving both stationary and nonstationary interpolation problems, in finite or infinite dimensions, based on the commutant lifting theorem from operator theory and the state space method from mathematical system theory. Initially the authors planned a number of papers treating nonstationary interpolation problems of Nevanlinna-Pick and Nehari type by reducing these nonstationary problems to stationary ones for operator-valued functions with operator arguments and using classical commutant lifting techniques. This reduction method required us to review and further develop the classical results for the stationary problems in this more general framework. Here the system theory turned out to be very useful for setting up the problems and for providing natural state space formulas for describing the solutions. In this way our work involved us in a much wider program than original planned. The final results of our efforts are presented here. The financial support in 1994 from the "NWO-stimulansprogramma" for the Thomas Stieltjes Institute for Mathematics in the Netherlands enabled us to start the research which lead to the present book. We also gratefully acknowledge the support from our home institutions: Indiana University at Bloomington, Purdue University at West Lafayette, Tel-Aviv University, and the Vrije Universiteit at Amsterdam. We warmly thank Dr. A.L. Sakhnovich for his carefully reading of a large part of the manuscript. Finally, Sharon Wise prepared very efficiently and with great care the troff file of this manuscript; we are grateful for her excellent typing.

Holomorphic Spaces

Author : Sheldon Jay Axler
Publisher : Cambridge University Press
ISBN 13 : 9780521631938
Total Pages : 490 pages
Book Rating : 4.6/5 (319 download)

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Book Synopsis Holomorphic Spaces by : Sheldon Jay Axler

Download or read book Holomorphic Spaces written by Sheldon Jay Axler and published by Cambridge University Press. This book was released on 1998-05-28 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expository articles describing the role Hardy spaces, Bergman spaces, Dirichlet spaces, and Hankel and Toeplitz operators play in modern analysis.

Featured Reviews in Mathematical Reviews 1997-1999

Author : Donald G. Babbitt
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896709
Total Pages : 762 pages
Book Rating : 4.8/5 (967 download)

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Book Synopsis Featured Reviews in Mathematical Reviews 1997-1999 by : Donald G. Babbitt

Download or read book Featured Reviews in Mathematical Reviews 1997-1999 written by Donald G. Babbitt and published by American Mathematical Soc.. This book was released on 2000-05-05 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of Featured Reviews makes available special detailed reviews of some of the most important mathematical articles and books published from 1997 through 1999. Also included are excellent reviews of several classic books and articles published prior to 1970. Among those reviews, for example, are the following: Homological Algebra by Henri Cartan and Samuel Eilenberg, reviewed by G. Hochschild; Faisceaux algebriques coherents by Jean-Pierre Serre, reviewed by C. Chevalley; and On the Theory of General Partial Differential Operators by Lars Hormander, reviewed by J. L. Lions. In particular, those seeking information on current developments outside their own area of expertise will find the volume very useful. By identifying some of the best publications, papers, and books that have had or are expected to have a significant impact in applied and pure mathematics, this volume will serve as a comprehensive guide to important new research across all fields covered by MR.

Interpolation, Schur Functions and Moment Problems II

Author : Daniel Alpay
Publisher : Springer Science & Business Media
ISBN 13 : 3034804288
Total Pages : 302 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Interpolation, Schur Functions and Moment Problems II by : Daniel Alpay

Download or read book Interpolation, Schur Functions and Moment Problems II written by Daniel Alpay and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of Schur analysis lie in a 1917 article by Issai Schur in which he constructed a numerical sequence to correspond to a holomorphic contractive function on the unit disk. These sequences are now known as Schur parameter sequences. Schur analysis has grown significantly since its beginnings in the early twentieth century and now encompasses a wide variety of problems related to several classes of holomorphic functions and their matricial generalizations. These problems include interpolation and moment problems as well as Schur parametrization of particular classes of contractive or nonnegative Hermitian block matrices. This book is primarily devoted to topics related to matrix versions of classical interpolation and moment problems. The major themes include Schur analysis of nonnegative Hermitian block Hankel matrices and the construction of Schur-type algorithms. This book also covers a number of recent developments in orthogonal rational matrix functions, matrix-valued Carathéodory functions and maximal weight solutions for particular matricial moment problems on the unit circle.

Recent Advances in Operator Theory

Author : A. Dijksma
Publisher : Birkhäuser
ISBN 13 : 3034883234
Total Pages : 592 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Recent Advances in Operator Theory by : A. Dijksma

Download or read book Recent Advances in Operator Theory written by A. Dijksma and published by Birkhäuser. This book was released on 2012-12-06 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of 25 papers dedicated to Israel Gohberg, an outstanding leader in operator theory. Also containing a review of his contributions to mathematics and a complete list of his publications. The book is of interest to a wide audience of pure and applied mathematicians.

Operator Theory in Different Settings and Related Applications

Author : Roland Duduchava
Publisher : Birkhäuser
ISBN 13 : 3319625276
Total Pages : 309 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Operator Theory in Different Settings and Related Applications by : Roland Duduchava

Download or read book Operator Theory in Different Settings and Related Applications written by Roland Duduchava and published by Birkhäuser. This book was released on 2018-03-28 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a selection of reports and survey articles on the latest research in the area of single and multivariable operator theory and related fields. The latter include singular integral equations, ordinary and partial differential equations, complex analysis, numerical linear algebra, and real algebraic geometry – all of which were among the topics presented at the 26th International Workshop in Operator Theory and its Applications, held in Tbilisi, Georgia, in the summer of 2015. Moreover, the volume includes three special commemorative articles. One of them is dedicated to the memory of Leiba Rodman, another to Murray Marshall, and a third to Boris Khvedelidze, an outstanding Georgian mathematician and one of the founding fathers of the theory of singular integral equations. The book will be of interest to a broad range of mathematicians, from graduate students to researchers, whose primary interests lie in operator theory, complex analysis and applications, as well as specialists in mathematical physics.

Mathematical Methods in Systems, Optimization, and Control

Author : Harry Dym
Publisher : Springer Science & Business Media
ISBN 13 : 3034804113
Total Pages : 370 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Mathematical Methods in Systems, Optimization, and Control by : Harry Dym

Download or read book Mathematical Methods in Systems, Optimization, and Control written by Harry Dym and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Bill Helton on the occasion of his sixty fifth birthday. It contains biographical material, a list of Bill's publications, a detailed survey of Bill's contributions to operator theory, optimization and control and 19 technical articles. Most of the technical articles are expository and should serve as useful introductions to many of the areas which Bill's highly original contributions have helped to shape over the last forty odd years. These include interpolation, Szegö limit theorems, Nehari problems, trace formulas, systems and control theory, convexity, matrix completion problems, linear matrix inequalities and optimization. The book should be useful to graduate students in mathematics and engineering, as well as to faculty and individuals seeking entry level introductions and references to the indicated topics. It can also serve as a supplementary text to numerous courses in pure and applied mathematics and engineering, as well as a source book for seminars.

Interpolation and Realization Theory with Applications to Control Theory

Author : Vladimir Bolotnikov
Publisher : Springer
ISBN 13 : 303011614X
Total Pages : 353 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Interpolation and Realization Theory with Applications to Control Theory by : Vladimir Bolotnikov

Download or read book Interpolation and Realization Theory with Applications to Control Theory written by Vladimir Bolotnikov and published by Springer. This book was released on 2019-04-08 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is devoted to Joseph A. (Joe) Ball’s contributions to operator theory and its applications and in celebration of his seventieth birthday. Joe Ball’s career spans over four and a half decades, starting with his work on model theory and related topics for non-contractions and operators on multiply connected domains. Later on, more applied operator theory themes appeared in his work, involving factorization and interpolation for operator-valued functions, with extensive applications in system and control theory. He has worked on nonlinear control, time-varying systems and, more recently, on multidimensional systems and noncommutative H∞-theory on the unit ball and polydisk, and more general domains, and these are only the main themes in his vast oeuvre. Fourteen research papers constitute the core of this volume, written by mathematicians who have collaborated with Joe or have been influenced by his vast mathematical work. A curriculum vitae, a publications list and a list of Joe Ball’s PhD students are included in this volume, as well as personal reminiscences by colleagues and friends. Contributions by Yu. M. Arlinskii, S. Hassi, M. Augat, J. W. Helton, I. Klep, S. McCullough, S. Balasubramanian, U. Wijesooriya, N. Cohen, Q. Fang, S. Gorai, J. Sarkar, G. J. Groenewald, S. ter Horst, J. Jaftha, A. C. M. Ran, M.A. Kaashoek, F. van Schagen, A. Kheifets, Z. A. Lykova, N. J. Young, A. E. Ajibo, R. T. W. Martin, A. Ramanantoanina, M.-J. Y. Ou, H. J. Woerdeman, A. van der Schaft, A. Tannenbaum, T. T. Georgiou, J. O. Deasy and L. Norton.

Operator Theory and Analysis

Author : H. Bart
Publisher : Birkhäuser
ISBN 13 : 3034882831
Total Pages : 460 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Operator Theory and Analysis by : H. Bart

Download or read book Operator Theory and Analysis written by H. Bart and published by Birkhäuser. This book was released on 2012-12-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: On November 12-14, 1997 a workshop was held at the Vrije Universiteit Amsterdam on the occasion of the sixtieth birthday ofM. A. Kaashoek. The present volume contains the proceedings of this workshop. The workshop was attended by 44 participants from all over the world: partici pants came from Austria, Belgium, Canada, Germany, Ireland, Israel, Italy, The Netherlands, South Africa, Switzerland, Ukraine and the USA. The atmosphere at the workshop was very warm and friendly. There where 21 plenary lectures, and each lecture was followed by a lively discussion. The workshop was supported by: the Vakgroep Wiskunde of the Vrije Univer siteit, the department of Mathematics and Computer Science of the Vrije Univer siteit, the Stichting VU Computer Science & Mathematics Research Centre, the Thomas Stieltjes Institute for Mathematics, and the department of Economics of the Erasmus University Rotterdam. The organizers would like to take this opportunity to express their gratitude for the support. Without it the workshop would not have been so successful as it was. Table of Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Photograph of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii Curriculum Vitae of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv List of Publications of M. A. Kaashoek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix l. Gohberg Opening Address . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxi H. Bart, A. C. M. Ran and H. I. Woerdeman Personal Reminiscences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxv V. Adamyan and R. Mennicken On the Separation of Certain Spectral Components of Selfadjoint Operator Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Conditions for the Separation of Spectral Components . . . . . . . 4 3. Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Recent Advances in Operator Theory and Its Applications

Author : Marinus A. Kaashoek
Publisher : Springer Science & Business Media
ISBN 13 : 3764373989
Total Pages : 478 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Recent Advances in Operator Theory and Its Applications by : Marinus A. Kaashoek

Download or read book Recent Advances in Operator Theory and Its Applications written by Marinus A. Kaashoek and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a selection of carefully refereed research papers, most of which were presented at the fourteenth International Workshop on Operator Theory and its Applications (IWOTA), held at Cagliari, Italy, from June 24-27, 2003. The papers, many of which have been written by leading experts in the field, concern a wide variety of topics in modern operator theory and applications, with emphasis on differential operators and numerical methods. The book will be of interest to a wide audience of pure and applied mathematicians and engineers.

Interpolation of Rational Matrix Functions

Author : Joseph Ball
Publisher : Birkhäuser
ISBN 13 : 3034877099
Total Pages : 605 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Interpolation of Rational Matrix Functions by : Joseph Ball

Download or read book Interpolation of Rational Matrix Functions written by Joseph Ball and published by Birkhäuser. This book was released on 2013-11-11 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an independent theory. After two years a major part of the first draft was prepared. Then a long period of revising the original draft and introducing recently acquired results and methods followed. There followed a period of polishing and of 25 chapters and the appendix commuting at various times somewhere between Williamsburg, Blacksburg, Tel Aviv, College Park and Amsterdam (sometimes with one or two of the authors).

Structured Matrices in Mathematics, Computer Science, and Engineering I

Author : Vadim Olshevsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821819216
Total Pages : pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Structured Matrices in Mathematics, Computer Science, and Engineering I by : Vadim Olshevsky

Download or read book Structured Matrices in Mathematics, Computer Science, and Engineering I written by Vadim Olshevsky and published by American Mathematical Soc.. This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topics in Operator Theory

Author : Joseph A. Ball
Publisher : Springer Science & Business Media
ISBN 13 : 3034601611
Total Pages : 446 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Topics in Operator Theory by : Joseph A. Ball

Download or read book Topics in Operator Theory written by Joseph A. Ball and published by Springer Science & Business Media. This book was released on 2011-02-03 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second volume of a collection of original and review articles on recent advances and new directions in a multifaceted and interconnected area of mathematics and its applications. It encompasses many topics in theoretical developments in operator theory and its diverse applications in applied mathematics, physics, engineering, and other disciplines. The purpose is to bring in one volume many important original results of cutting edge research as well as authoritative review of recent achievements, challenges, and future directions in the area of operator theory and its applications.

Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations

Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3319688499
Total Pages : 495 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations by : Daniel Alpay

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.

Interpolation Theory, Systems Theory and Related Topics

Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3034882157
Total Pages : 420 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Interpolation Theory, Systems Theory and Related Topics by : Daniel Alpay

Download or read book Interpolation Theory, Systems Theory and Related Topics written by Daniel Alpay and published by Birkhäuser. This book was released on 2012-12-06 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Harry Dym, a leading expert in operator theory, on the occasion of his sixtieth birthday. The book opens with an autobiographical sketch, a list of publications and a personal account of I. Gohberg on his collaboration with Harry Dym. The mathematical papers cover Krein space operator theory, Schur analysis and interpolation, several complex variables and Riemann surfaces, matrix theory, system theory, and differential equations and mathematical physics. The book is of interest to a wide audience of pure and applied mathematicians, electrical engineers and theoretical physicists.

The Schur Algorithm, Reproducing Kernel Spaces and System Theory

Author : Daniel Alpay
Publisher : American Mathematical Soc.
ISBN 13 : 9780821821558
Total Pages : 162 pages
Book Rating : 4.8/5 (215 download)

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Book Synopsis The Schur Algorithm, Reproducing Kernel Spaces and System Theory by : Daniel Alpay

Download or read book The Schur Algorithm, Reproducing Kernel Spaces and System Theory written by Daniel Alpay and published by American Mathematical Soc.. This book was released on 2001 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The class of Schur functions consists of analytic functions on the unit disk that are bounded by $1$. The Schur algorithm associates to any such function a sequence of complex constants, which is much more useful than the Taylor coefficients. There is a generalization to matrix-valued functions and a corresponding algorithm. These generalized Schur functions have important applications to the theory of linear operators, to signal processing and control theory, and to other areas of engineering. 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. The inverse scattering problem plays a key role in the exposition. The point of view also allows for a natural way to tackle more general cases, such as nonstationary systems, non-positive metrics, and pairs of commuting nonself-adjoint operators. This is the English translation of a volume originally published in French by the Societe Mathematique de France. Translated by Stephen S. Wilson.