Indefinite Inner Product Spaces Schur Analysis And Differential Equations

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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 : 49,8 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.

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 : 46,5 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.

Operator Theory and Indefinite Inner Product Spaces

Matthias Langer,Annemarie Luger,Harald Woracek
Operator Theory and Indefinite Inner Product Spaces Book PDF

Author : Matthias Langer,Annemarie Luger,Harald Woracek
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 40,9 Mb
Release : 2006-06-16
Category : Mathematics
ISBN : 9783764375164

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Operator Theory and Indefinite Inner Product Spaces by Matthias Langer,Annemarie Luger,Harald Woracek Pdf

A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.

Interpolation and Realization Theory with Applications to Control Theory

Vladimir Bolotnikov,Sanne ter Horst,André C.M. Ran,Victor Vinnikov
Interpolation and Realization Theory with Applications to Control Theory Book PDF

Author : Vladimir Bolotnikov,Sanne ter Horst,André C.M. Ran,Victor Vinnikov
Publisher : Springer
Page : 353 pages
File Size : 50,8 Mb
Release : 2019-04-08
Category : Mathematics
ISBN : 9783030116149

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Interpolation and Realization Theory with Applications to Control Theory by Vladimir Bolotnikov,Sanne ter Horst,André C.M. Ran,Victor Vinnikov Pdf

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.

Indefinite Inner Product Spaces

J. Bognar
Indefinite Inner Product Spaces Book PDF

Author : J. Bognar
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642655678

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Indefinite Inner Product Spaces by J. Bognar Pdf

By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi tian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values. The most important special case arises when a Hilbert space is considered as an orthogonal direct sum of two subspaces, one equipped with the original inner prod uct, and the other with -1 times the original inner product. The subject first appeared thirty years ago in a paper of Dirac [1] on quantum field theory (d. also Pauli [lJ). Soon afterwards, Pontrja gin [1] gave the first mathematical treatment of an indefinite inner prod uct space. Pontrjagin was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics. The attempts of Dirac and Pauli to apply the concept and elemen tary properties of indefinite inner product spaces to field theory have been renewed by several authors. At present it is not easy to judge which of their results will contribute to the final form of this part of physics. The following list of references should serve as a guide to the extensive literature: Bleuler [1], Gupta [lJ, Kallen and Pauli [lJ, Heisen berg [lJ-[4J, Bogoljubov, Medvedev and Polivanov [lJ, K.L. Nagy [lJ-[3], Berezin [lJ, Arons, Han and Sudarshan [1], Lee and Wick [1J.

Current Trends in Operator Theory and its Applications

Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman
Current Trends in Operator Theory and its Applications Book PDF

Author : Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman
Publisher : Birkhäuser
Page : 604 pages
File Size : 52,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034878814

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Current Trends in Operator Theory and its Applications by Joseph A. Ball,J. William Helton,Martin Klaus,Leiba Rodman Pdf

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.

Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes

Daniel Alpay,Bernd Kirstein
Recent Advances in Inverse Scattering Schur Analysis and Stochastic Processes Book PDF

Author : Daniel Alpay,Bernd Kirstein
Publisher : Birkhäuser
Page : 394 pages
File Size : 46,7 Mb
Release : 2015-04-30
Category : Mathematics
ISBN : 9783319103358

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Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes by Daniel Alpay,Bernd Kirstein Pdf

The volume is dedicated to Lev Sakhnovich, who made fundamental contributions in operator theory and related topics. Besides bibliographic material, it includes a number of selected papers related to Lev Sakhnovich's research interests. The papers are related to operator identities, moment problems, random matrices and linear stochastic systems.

Operator Theory and Indefinite Inner Product Spaces

Matthias Langer,Annemarie Luger,Harald Woracek
Operator Theory and Indefinite Inner Product Spaces Book PDF

Author : Matthias Langer,Annemarie Luger,Harald Woracek
Publisher : Birkhäuser
Page : 381 pages
File Size : 40,5 Mb
Release : 2009-09-03
Category : Mathematics
ISBN : 3764391073

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Operator Theory and Indefinite Inner Product Spaces by Matthias Langer,Annemarie Luger,Harald Woracek Pdf

A colloquium on operator theory was held in Vienna, Austria, in March 2004, on the occasion of the retirement of Heinz Langer, a leading expert in operator theory and indefinite inner product spaces. The book contains fifteen refereed articles reporting on recent and original results in various areas of operator theory, all of them related with the work of Heinz Langer. The topics range from abstract spectral theory in Krein spaces to more concrete applications, such as boundary value problems, the study of orthogonal functions, or moment problems. The book closes with a historical survey paper.

Recent Developments in Mathematical, Statistical and Computational Sciences

D. Marc Kilgour,Herb Kunze,Roman Makarov,Roderick Melnik,Xu Wang
Recent Developments in Mathematical Statistical and Computational Sciences Book PDF

Author : D. Marc Kilgour,Herb Kunze,Roman Makarov,Roderick Melnik,Xu Wang
Publisher : Springer Nature
Page : 728 pages
File Size : 53,8 Mb
Release : 2021-08-29
Category : Mathematics
ISBN : 9783030635916

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Recent Developments in Mathematical, Statistical and Computational Sciences by D. Marc Kilgour,Herb Kunze,Roman Makarov,Roderick Melnik,Xu Wang Pdf

This book constitutes an up-to-date account of principles, methods, and tools for mathematical and statistical modelling in a wide range of research fields, including medicine, health sciences, biology, environmental science, engineering, physics, chemistry, computation, finance, economics, and social sciences. It presents original solutions to real-world problems, emphasizes the coordinated development of theories and applications, and promotes interdisciplinary collaboration among mathematicians, statisticians, and researchers in other disciplines. Based on a highly successful meeting, the International Conference on Applied Mathematics, Modeling and Computational Science, AMMCS 2019, held from August 18 to 23, 2019, on the main campus of Wilfrid Laurier University, Waterloo, Canada, the contributions are the results of submissions from the conference participants. They provide readers with a broader view of the methods, ideas and tools used in mathematical, statistical and computational sciences.

Harmonic Analysis and Operator Theory

Mischa Cotlar,Stefania A. M. Marcantognini
Harmonic Analysis and Operator Theory Book PDF

Author : Mischa Cotlar,Stefania A. M. Marcantognini
Publisher : American Mathematical Soc.
Page : 511 pages
File Size : 53,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821803042

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Harmonic Analysis and Operator Theory by Mischa Cotlar,Stefania A. M. Marcantognini Pdf

This book is a collection of papers reflecting the conference held in Caracas, Venezuela, in January 1994 in celebration of Professor Mischa Cotlar's eightieth birthday. Presenting an excellent account of recent advances in harmonic analysis and operator theory and their applications, many of the contributors are world leaders in their fields. The collection covers a broad spectrum of topics, including: wavelet analysis, Haenkel operators, multimeasure theory, the boundary behavior of the Bergman kernel, interpolation theory, and Cotlar's Lemma on almost orthogonality in the context of L[superscript p] spaces and more... The range of topics in this volume promotes cross-pollination among the various fields covered. Such variety makes "Harmonic Analysis and Operator Theory" an inspiration for graduate students interested in this area of study.

Inner Product Spaces and Applications

T M Rassias
Inner Product Spaces and Applications Book PDF

Author : T M Rassias
Publisher : CRC Press
Page : 284 pages
File Size : 54,6 Mb
Release : 1997-10-08
Category : Mathematics
ISBN : 0582317118

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Inner Product Spaces and Applications by T M Rassias Pdf

In this volume, the contributing authors deal primarily with the interaction among problems of analysis and geometry in the context of inner product spaces. They present new and old characterizations of inner product spaces among normed linear spaces and the use of such spaces in various research problems of pure and applied mathematics. The methods employed are accessible to students familiar with normed linear spaces. Some of the theorems presented are at the same time simple and challenging.

Contributions to Operator Theory in Spaces with an Indefinite Metric

Aad Dijksma,Israel Gohberg,Marinus A. Kaashoek,Reinhard Mennicken
Contributions to Operator Theory in Spaces with an Indefinite Metric Book PDF

Author : Aad Dijksma,Israel Gohberg,Marinus A. Kaashoek,Reinhard Mennicken
Publisher : Birkhäuser
Page : 419 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034888127

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Contributions to Operator Theory in Spaces with an Indefinite Metric by Aad Dijksma,Israel Gohberg,Marinus A. Kaashoek,Reinhard Mennicken Pdf

This volume is dedicated to Heinz Langer, a leading expert in spectral analysis and its applications, in particular to operators in spaces with an indefinite metric, on the occasion of his 60th birthday. The book begins with his biography and list of publications. It contains a selection of research papers, most of which are devoted to spectral analysis of operators or operator pencils with applications to ordinary and partial differential equations. Other papers deal with time-varying systems, interpolation and factorization problems, and topics from mathematical physics. About half of the papers contain further developments in the theory of operators in spaces with an indefinite metric and treat new applications. The book is of interest to a wide audience of pure and applied mathematicians.

Analysis and Partial Differential Equations

Cora Sadosky
Analysis and Partial Differential Equations Book PDF

Author : Cora Sadosky
Publisher : CRC Press
Page : 792 pages
File Size : 53,7 Mb
Release : 1989-12-15
Category : Mathematics
ISBN : 0849306531

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Analysis and Partial Differential Equations by Cora Sadosky Pdf

This book provides a descriptive account of Mischa Cotlar's work along with a complete bibliography of his mathematical books and papers. It examines the harmonic analysis and operator theory in relation with the theory of partial differential equations.

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

Peter Benner,Matthias Bollhöfer,Daniel Kressner,Christian Mehl,Tatjana Stykel
Numerical Algebra Matrix Theory Differential Algebraic Equations and Control Theory Book PDF

Author : Peter Benner,Matthias Bollhöfer,Daniel Kressner,Christian Mehl,Tatjana Stykel
Publisher : Springer
Page : 608 pages
File Size : 53,9 Mb
Release : 2015-05-09
Category : Mathematics
ISBN : 9783319152608

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Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory by Peter Benner,Matthias Bollhöfer,Daniel Kressner,Christian Mehl,Tatjana Stykel Pdf

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.

The Schur Algorithm, Reproducing Kernel Spaces and System Theory

Daniel Alpay
The Schur Algorithm Reproducing Kernel Spaces and System Theory Book PDF

Author : Daniel Alpay
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 50,8 Mb
Release : 2001
Category : Computers
ISBN : 0821821555

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The Schur Algorithm, Reproducing Kernel Spaces and System Theory by Daniel Alpay Pdf

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.