Metric Constrained Interpolation Commutant Lifting And Systems

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Metric Constrained Interpolation, Commutant Lifting and Systems

C. Foias,A.E. Frezho,I. Gohberg,M.A. Kaashoek
Metric Constrained Interpolation Commutant Lifting and Systems Book PDF

Author : C. Foias,A.E. Frezho,I. Gohberg,M.A. Kaashoek
Publisher : Birkhäuser
Page : 587 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887915

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Metric Constrained Interpolation, Commutant Lifting and Systems by C. Foias,A.E. Frezho,I. Gohberg,M.A. Kaashoek Pdf

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.

Mathematical Methods in Systems, Optimization, and Control

Harry Dym,Mauricio C. de Oliveira,Mihai Putinar
Mathematical Methods in Systems Optimization and Control Book PDF

Author : Harry Dym,Mauricio C. de Oliveira,Mihai Putinar
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 40,8 Mb
Release : 2012-07-25
Category : Mathematics
ISBN : 9783034804110

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Mathematical Methods in Systems, Optimization, and Control by Harry Dym,Mauricio C. de Oliveira,Mihai Putinar Pdf

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.

Linear Operators and Linear Systems

Jonathan R. Partington
Linear Operators and Linear Systems Book PDF

Author : Jonathan R. Partington
Publisher : Cambridge University Press
Page : 184 pages
File Size : 43,7 Mb
Release : 2004-03-15
Category : Mathematics
ISBN : 0521546192

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Linear Operators and Linear Systems by Jonathan R. Partington Pdf

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Operator Theory in Different Settings and Related Applications

Roland Duduchava,Marinus A. Kaashoek,Nikolai Vasilevski,Victor Vinnikov
Operator Theory in Different Settings and Related Applications Book PDF

Author : Roland Duduchava,Marinus A. Kaashoek,Nikolai Vasilevski,Victor Vinnikov
Publisher : Birkhäuser
Page : 309 pages
File Size : 48,6 Mb
Release : 2018-03-28
Category : Mathematics
ISBN : 9783319625270

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Operator Theory in Different Settings and Related Applications by Roland Duduchava,Marinus A. Kaashoek,Nikolai Vasilevski,Victor Vinnikov Pdf

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.

Recent Advances in Robust Control

Andreas Müller
Recent Advances in Robust Control Book PDF

Author : Andreas Müller
Publisher : BoD – Books on Demand
Page : 412 pages
File Size : 43,5 Mb
Release : 2011-11-21
Category : Science
ISBN : 9789533074214

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Recent Advances in Robust Control by Andreas Müller Pdf

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics.

Nigel J. Kalton Selecta

Fritz Gesztesy,Gilles Godefroy,Loukas Grafakos,Igor Verbitsky
Nigel J Kalton Selecta Book PDF

Author : Fritz Gesztesy,Gilles Godefroy,Loukas Grafakos,Igor Verbitsky
Publisher : Birkhäuser
Page : 771 pages
File Size : 42,9 Mb
Release : 2016-07-05
Category : Mathematics
ISBN : 9783319187969

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Nigel J. Kalton Selecta by Fritz Gesztesy,Gilles Godefroy,Loukas Grafakos,Igor Verbitsky Pdf

This book is the first part of a two volume anthology comprising a selection of 49 articles that illustrate the depth, breadth and scope of Nigel Kalton’s research. Each article is accompanied by comments from an expert on the respective topic, which serves to situate the article in its proper context, to successfully link past, present and hopefully future developments of the theory, and to help readers grasp the extent of Kalton’s accomplishments. Kalton’s work represents a bridge to the mathematics of tomorrow, and this book will help readers to cross it. Nigel Kalton (1946-2010) was an extraordinary mathematician who made major contributions to an amazingly diverse range of fields over the course of his career.

Recent Advances in Operator Theory and Its Applications

Marinus A. Kaashoek,Sebastiano Seatzu,Cornelis van der Mee
Recent Advances in Operator Theory and Its Applications Book PDF

Author : Marinus A. Kaashoek,Sebastiano Seatzu,Cornelis van der Mee
Publisher : Springer Science & Business Media
Page : 478 pages
File Size : 47,8 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373986

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Recent Advances in Operator Theory and Its Applications by Marinus A. Kaashoek,Sebastiano Seatzu,Cornelis van der Mee Pdf

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.

Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations

Daniel Alpay,Bernd Kirstein
Indefinite Inner Product Spaces Schur Analysis and Differential Equations Book PDF

Author : Daniel Alpay,Bernd Kirstein
Publisher : Birkhäuser
Page : 495 pages
File Size : 46,8 Mb
Release : 2018-01-30
Category : Mathematics
ISBN : 9783319688497

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Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations by Daniel Alpay,Bernd Kirstein Pdf

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

Daniel Alpay,Israel Gohberg,Victor Vinnikov
Interpolation Theory Systems Theory and Related Topics Book PDF

Author : Daniel Alpay,Israel Gohberg,Victor Vinnikov
Publisher : Birkhäuser
Page : 420 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882156

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Interpolation Theory, Systems Theory and Related Topics by Daniel Alpay,Israel Gohberg,Victor Vinnikov Pdf

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.

Operator Theory, Analysis and the State Space Approach

Harm Bart,Sanne ter Horst,André C.M. Ran,Hugo J. Woerdeman
Operator Theory Analysis and the State Space Approach Book PDF

Author : Harm Bart,Sanne ter Horst,André C.M. Ran,Hugo J. Woerdeman
Publisher : Springer
Page : 464 pages
File Size : 42,7 Mb
Release : 2018-12-30
Category : Mathematics
ISBN : 9783030042691

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Operator Theory, Analysis and the State Space Approach by Harm Bart,Sanne ter Horst,André C.M. Ran,Hugo J. Woerdeman Pdf

This volume is dedicated to Rien Kaashoek on the occasion of his 80th birthday and celebrates his many contributions to the field of operator theory during more than fifty years. In the first part of the volume, biographical information and personal accounts on the life of Rien Kaashoek are presented. Eighteen research papers by friends and colleagues of Rien Kaashoek are included in the second part. Contributions by J. Agler, Z.A. Lykova, N.J. Young, J.A. Ball, G.J. Groenewald, S. ter Horst, H. Bart, T. Ehrhardt, B. Silbermann, J.M. Bogoya, S.M. Grudsky, I.S. Malysheva, A. Böttcher, E. Wegert, Z. Zhou, Y. Eidelman, I. Haimovici, A.E. Frazho, A.C.M. Ran, B. Fritzsche, B. Kirstein, C.Madler, J. J. Jaftha, D.B. Janse van Rensburg, P. Junghanns, R. Kaiser, J. Nemcova, M. Petreczky, J.H. van Schuppen, L. Plevnik, P. Semrl, A. Sakhnovich, F.-O. Speck, S. Sremac, H.J. Woerdeman, H. Wolkowicz and N. Vasilevski.

Interpolation, Schur Functions and Moment Problems II

Daniel Alpay,Bernd Kirstein
Interpolation Schur Functions and Moment Problems II Book PDF

Author : Daniel Alpay,Bernd Kirstein
Publisher : Springer Science & Business Media
Page : 302 pages
File Size : 54,9 Mb
Release : 2012-07-25
Category : Mathematics
ISBN : 9783034804288

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Interpolation, Schur Functions and Moment Problems II by Daniel Alpay,Bernd Kirstein Pdf

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.​

Dynamical Systems, Control, Coding, Computer Vision

Giorgio Picci,D.S. Gilliam
Dynamical Systems Control Coding Computer Vision Book PDF

Author : Giorgio Picci,D.S. Gilliam
Publisher : Birkhäuser
Page : 498 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034889704

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Dynamical Systems, Control, Coding, Computer Vision by Giorgio Picci,D.S. Gilliam Pdf

This book is a collection of essays devoted in part to new research direc tions in systems, networks, and control theory, and in part to the growing interaction of these disciplines with new sectors of engineering and applied sciences like coding, computer vision, and hybrid systems. These are new areas of rapid growth and of increasing importance in modern technology. The essays, written by world-leading experts in the field, reproduce and expand the plenary and minicoursejminisymposia invited lectures which were delivered at the Mathematical Theory of Networks and Systems Sym posium (MTNS-98), held in Padova, Italy, on July 6-10, 1998. Systems, control, and networks theory has permeated the development of much of present day technology. The impact has been visible in the past fifty years through the dramatic expansion and achievements of the aerospace and avionics industry, through process control and factory au tomation, robotics, communication signals analysis and synthesis, and, more recently, even finance, to name just the most visible applications. The theory has developed from the early phase of its history when the ba sic tools were elementary complex analysis, Laplace transform, and linear differential equations, to present day, where the mathematics ranges widely from functional analysis, PDE's, abstract algebra, stochastic processes and differential geometry. Irrespective of the particular tools, however, the ba sic unifying paradigms of feedback, stability, optimal control, and recursive filtering, have remained the bulk of the field and continue to be the basic motivation for the theory, coming from the real world.

Topics in Operator Theory

Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky
Topics in Operator Theory Book PDF

Author : Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 49,7 Mb
Release : 2011-02-03
Category : Mathematics
ISBN : 9783034601610

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Topics in Operator Theory by Joseph A. Ball,Vladimir Bolotnikov,J. William Helton,Leiba Rodman,Ilya M. Spitkovsky Pdf

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.

Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis

Daniel Alpay,Jussi Behrndt,Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa
Recent Developments in Operator Theory Mathematical Physics and Complex Analysis Book PDF

Author : Daniel Alpay,Jussi Behrndt,Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa
Publisher : Springer Nature
Page : 424 pages
File Size : 42,6 Mb
Release : 2023-04-11
Category : Mathematics
ISBN : 9783031214608

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Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis by Daniel Alpay,Jussi Behrndt,Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa Pdf

This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.

An Operator Perspective on Signals and Systems

Arthur Frazho,Wisuwat Bhosri
An Operator Perspective on Signals and Systems Book PDF

Author : Arthur Frazho,Wisuwat Bhosri
Publisher : Springer Science & Business Media
Page : 430 pages
File Size : 47,5 Mb
Release : 2009-12-29
Category : Mathematics
ISBN : 9783034602921

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An Operator Perspective on Signals and Systems by Arthur Frazho,Wisuwat Bhosri Pdf

In this monograph, we combine operator techniques with state space methods to solve factorization, spectral estimation, and interpolation problems arising in control and signal processing. We present both the theory and algorithms with some Matlab code to solve these problems. A classical approach to spectral factorization problems in control theory is based on Riccati equations arising in linear quadratic control theory and Kalman ?ltering. One advantage of this approach is that it readily leads to algorithms in the non-degenerate case. On the other hand, this approach does not easily generalize to the nonrational case, and it is not always transparent where the Riccati equations are coming from. Operator theory has developed some elegant methods to prove the existence of a solution to some of these factorization and spectral estimation problems in a very general setting. However, these techniques are in general not used to develop computational algorithms. In this monograph, we will use operator theory with state space methods to derive computational methods to solve factorization, sp- tral estimation, and interpolation problems. It is emphasized that our approach is geometric and the algorithms are obtained as a special application of the theory. We will present two methods for spectral factorization. One method derives al- rithms based on ?nite sections of a certain Toeplitz matrix. The other approach uses operator theory to develop the Riccati factorization method. Finally, we use isometric extension techniques to solve some interpolation problems.