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Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations

Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations
Author: Daniel Alpay
Publisher: Birkhäuser
Total Pages: 501
Release: 2018-01-30
Genre: Mathematics
ISBN: 3319688499

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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

Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis
Author: Daniel Alpay
Publisher: Springer Nature
Total Pages: 424
Release: 2023-04-11
Genre: Mathematics
ISBN: 3031214609

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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.


Interpolation and Realization Theory with Applications to Control Theory

Interpolation and Realization Theory with Applications to Control Theory
Author: Vladimir Bolotnikov
Publisher: Springer
Total Pages: 353
Release: 2019-04-08
Genre: Mathematics
ISBN: 303011614X

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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.


Recent Developments in Mathematical, Statistical and Computational Sciences

Recent Developments in Mathematical, Statistical and Computational Sciences
Author: D. Marc Kilgour
Publisher: Springer Nature
Total Pages: 728
Release: 2021-08-29
Genre: Mathematics
ISBN: 3030635910

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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.


Current Trends in Operator Theory and its Applications

Current Trends in Operator Theory and its Applications
Author: Joseph A. Ball
Publisher: Birkhäuser
Total Pages: 604
Release: 2012-12-06
Genre: Mathematics
ISBN: 3034878818

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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

Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes
Author: Daniel Alpay
Publisher: Birkhäuser
Total Pages: 396
Release: 2015-04-30
Genre: Mathematics
ISBN: 3319103350

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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.


Harmonic Analysis and Operator Theory

Harmonic Analysis and Operator Theory
Author: Stefania A. M. Marcantognini
Publisher: American Mathematical Soc.
Total Pages: 528
Release: 1995
Genre: Mathematics
ISBN: 0821803042

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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...


Analysis and Partial Differential Equations

Analysis and Partial Differential Equations
Author: Cora Sadosky
Publisher: CRC Press
Total Pages: 785
Release: 1989-12-15
Genre: Mathematics
ISBN: 1482276925

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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

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory
Author: Peter Benner
Publisher: Springer
Total Pages: 635
Release: 2015-05-09
Genre: Mathematics
ISBN: 3319152602

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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.


Operator Theory and Indefinite Inner Product Spaces

Operator Theory and Indefinite Inner Product Spaces
Author: Matthias Langer
Publisher: Springer Science & Business Media
Total Pages: 403
Release: 2006-06-16
Genre: Mathematics
ISBN: 3764375167

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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.