Hankel Operators And Their Applications
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Hankel Operators And Their Applications
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Author : Vladimir Peller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hankel Operators And Their Applications written by Vladimir Peller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The purpose of this book is to describe the theory of Hankel operators, one of the most important classes of operators on spaces of analytic func tions. Hankel operators can be defined as operators having infinite Hankel matrices (i. e. , matrices with entries depending only on the sum of the co ordinates) with respect to some orthonormal basis. Finite matrices with this property were introduced by Hankel, who found interesting algebraic properties of their determinants. One of the first results on infinite Han kel matrices was obtained by Kronecker, who characterized Hankel matri ces of finite rank as those whose entries are Taylor coefficients of rational functions. Since then Hankel operators (or matrices) have found numerous applications in classical problems of analysis, such as moment problems, orthogonal polynomials, etc. Hankel operators admit various useful realizations, such as operators on spaces of analytic functions, integral operators on function spaces on (0,00), operators on sequence spaces. In 1957 Nehari described the bounded Hankel operators on the sequence space £2. This description turned out to be very important and started the contemporary period of the study of Hankel operators. We begin the book with introductory Chapter 1, which defines Hankel operators and presents their basic properties. We consider different realiza tions of Hankel operators and important connections of Hankel operators with the spaces BMa and V MO, Sz. -Nagy-Foais functional model, re producing kernels of the Hardy class H2, moment problems, and Carleson imbedding operators.
Hankel Operators And Their Applications
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Author :
language : en
Publisher:
Release Date : 2011
Hankel Operators And Their Applications written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Hankel Operators And Their Applications
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Author : Vladimir Peller
language : en
Publisher:
Release Date : 2003-01-14
Hankel Operators And Their Applications written by Vladimir Peller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-14 with categories.
An Introduction To Hankel Operators
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Author : Jonathan R. Partington
language : en
Publisher: Cambridge University Press
Release Date : 1988
An Introduction To Hankel Operators written by Jonathan R. Partington and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
Hankel operators are of wide application in mathematics and engineering and this account of them is both elementary and rigorous.
An Introduction To Operators On The Hardy Hilbert Space
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Author : Ruben A. Martinez-Avendano
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-12
An Introduction To Operators On The Hardy Hilbert Space written by Ruben A. Martinez-Avendano and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-12 with Mathematics categories.
This book offers an elementary and engaging introduction to operator theory on the Hardy-Hilbert space. It provides a firm foundation for the study of all spaces of analytic functions and of the operators on them. Blending techniques from "soft" and "hard" analysis, the book contains clear and beautiful proofs. There are numerous exercises at the end of each chapter, along with a brief guide for further study which includes references to applications to topics in engineering.
Analysis Of Toeplitz Operators
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Author : Albrecht Böttcher
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-11
Analysis Of Toeplitz Operators written by Albrecht Böttcher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-11 with Mathematics categories.
Since the late 1980s, Toeplitz operators and matrices have remained a ?eld of extensive research and the development during the last nearly twenty years is impressive. One encounters Toeplitz matrices in plenty of applications on the one hand, and Toeplitz operators con?rmed their role as the basic elementary building blocks of more complicated operators on the other. Several monographs on Toeplitz and Hankel operators were written d- ing the last decade. These include Peller’s grandiose book on Hankel ope- tors and their applications and Nikolski’s beautiful easy reading on operators, functions, and systems, with emphasis on topics connected with the names of Hardy, Hankel, and Toeplitz. They also include books by the authors together withHagen,Roch,Yu.Karlovich,Spitkovsky,Grudsky,andRabinovich.Thus, results, techniques, and developments in the ?eld of Toeplitz operators are now well presented in the monographic literature. Despite these competitive works, we felt that large parts of the ?rst edition of the present monograp- whichismeanwhileoutofstock-havenotlosttheirfascinationandrelevance. Moreover, the ?rst edition has received a warm reception by many colleagues and became a standard reference. This encouraged us to venture on thinking about a second edition, and we are grateful to the Springer Publishing House for showing an interest in this.
Operator Theory Functional Analysis And Applications
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Author : M. Amélia Bastos
language : en
Publisher: Springer Nature
Release Date : 2021-03-31
Operator Theory Functional Analysis And Applications written by M. Amélia Bastos and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-31 with Mathematics categories.
This book presents 30 articles on the topic areas discussed at the 30th “International Workshop on Operator Theory and its Applications”, held in Lisbon in July 2019. The contributions include both expository essays and original research papers reflecting recent advances in the traditional IWOTA areas and emerging adjacent fields, as well as the applications of Operator Theory and Functional Analysis. The topics range from C*–algebras and Banach *–algebras, Sturm-Liouville theory, integrable systems, dilation theory, frame theory, Toeplitz, Hankel, and singular integral operators, to questions from lattice, group and matrix theories, complex analysis, harmonic analysis, and function spaces. Given its scope, the book is chiefly intended for researchers and graduate students in the areas of Operator Theory, Functional Analysis, their applications and adjacent fields.
Harmonic Analysis In Operator Algebras And Its Applications To Index Theory And Topological Solid State Systems
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Author : Hermann Schulz-Baldes
language : en
Publisher: Springer Nature
Release Date : 2022-12-31
Harmonic Analysis In Operator Algebras And Its Applications To Index Theory And Topological Solid State Systems written by Hermann Schulz-Baldes and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-31 with Science categories.
This book contains a self-consistent treatment of Besov spaces for W*-dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*-crossed product algebra. These criteria allow to extend index theorems to such operator classes. This in turn is of great relevance for applications in solid-state physics, in particular, Anderson localized topological insulators as well as topological semimetals. The book also contains a self-contained chapter on duality theory for R-actions. It allows to prove a bulk-boundary correspondence for boundaries with irrational angles which implies the existence of flat bands of edge states in graphene-like systems. This book is intended for advanced students in mathematical physics and researchers alike.
Lectures On Analytic Function Spaces And Their Applications
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Author : Javad Mashreghi
language : en
Publisher: Springer Nature
Release Date : 2023-10-13
Lectures On Analytic Function Spaces And Their Applications written by Javad Mashreghi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-13 with Mathematics categories.
The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They have essential applications in other fields of mathematics and engineering. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins—the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b)—have also garnered attention in recent decades. Leading experts on function spaces gathered and discussed new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With over 250 hours of lectures by prominent mathematicians, the program spanned a wide variety of topics. More explicitly, there were courses and workshops on Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Blaschke Products and Inner Functions, and Convergence of Scattering Data and Non-linear Fourier Transform, among others. At the end of each week, there was a high-profile colloquium talk on the current topic. The program also contained two advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. This volume features the courses given on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Semigroups of weighted composition operators on spaces of holomorphic functions, the Corona Problem, Non-commutative Function Theory, and Drury-Arveson Space. This volume is a valuable resource for researchers interested in analytic function spaces.
Operator Theory Operator Algebras And Matrix Theory
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Author : Carlos André
language : en
Publisher: Birkhäuser
Release Date : 2018-08-22
Operator Theory Operator Algebras And Matrix Theory written by Carlos André and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-22 with Mathematics categories.
This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.