Harmonic Analysis In Operator Algebras And Its Applications To Index Theory And Topological Solid State Systems

Harmonic Analysis In Operator Algebras And Its Applications To Index Theory And Topological Solid State Systems Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Harmonic Analysis In Operator Algebras And Its Applications To Index Theory And Topological Solid State Systems book. This book definitely worth reading, it is an incredibly well-written.

Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems

Hermann Schulz-Baldes,Tom Stoiber
Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems Book PDF

Author : Hermann Schulz-Baldes,Tom Stoiber
Publisher : Springer Nature
Page : 225 pages
File Size : 48,6 Mb
Release : 2022-12-31
Category : Science
ISBN : 9783031122019

Get Book

Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems by Hermann Schulz-Baldes,Tom Stoiber Pdf

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.

Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics

Wolfgang Arendt,Ralph Chill,Yuri Tomilov
Operator Semigroups Meet Complex Analysis Harmonic Analysis and Mathematical Physics Book PDF

Author : Wolfgang Arendt,Ralph Chill,Yuri Tomilov
Publisher : Birkhäuser
Page : 496 pages
File Size : 40,5 Mb
Release : 2015-12-10
Category : Mathematics
ISBN : 9783319184944

Get Book

Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics by Wolfgang Arendt,Ralph Chill,Yuri Tomilov Pdf

This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern semigroup theory, harmonic analysis, complex analysis and mathematical physics, and to present the lively interactions between all of those areas and beyond. In addition, the meeting honored the sixtieth anniversary of Prof C. J. K. Batty, whose scientific achievements are an impressive illustration of the conference goal. These proceedings present contributions by prominent scientists at this international conference, which became a landmark event. They will be a valuable and inspiring source of information for graduate students and established researchers.

Harmonic Analysis in Hypercomplex Systems

Yu.M. Berezansky,A.A. Kalyuzhnyi
Harmonic Analysis in Hypercomplex Systems Book PDF

Author : Yu.M. Berezansky,A.A. Kalyuzhnyi
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 47,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401717588

Get Book

Harmonic Analysis in Hypercomplex Systems by Yu.M. Berezansky,A.A. Kalyuzhnyi Pdf

First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operators that generalize usual translation operators were investigated and the corresponding harmonic analysis was constructed. Later, starting from 1950, it was noticed that, in such constructions, an important role is played by the fact that the kernels of the corresponding convolutions of functions are nonnegative and by the properties of the normed algebras generated by these convolutions. That was the way the notion of hypercomplex system with continu ous basis appeared. A hypercomplex system is a normed algebra of functions on a locally compact space Q-the "basis" of this hypercomplex system. Later, similar objects, hypergroups, were introduced, which have complex-valued measures on Q as elements and convolution defined to be essentially the convolution of functionals and dual to the original convolution (if measures are regarded as functionals on the space of continuous functions on Q). However, until 1991, the time when this book was written in Russian, there were no monographs containing fundamentals of the theory (with an exception of a short section in the book by Yu. M. Berezansky and Yu. G. Kondratiev [BeKo]). The authors wanted to give an introduction to the theory and cover the most important subsequent results and examples.

Operator Algebras and Quantum Statistical Mechanics

Ola Bratteli,Derek William Robinson
Operator Algebras and Quantum Statistical Mechanics Book PDF

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 43,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662023136

Get Book

Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli,Derek William Robinson Pdf

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission of various interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems offield theory and statistical mechanics. But the theory of 20 years ago was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

Abstract Harmonic Analysis

Edwin Hewitt,Kenneth Allen Ross
Abstract Harmonic Analysis Book PDF

Author : Edwin Hewitt,Kenneth Allen Ross
Publisher : Springer
Page : 527 pages
File Size : 52,5 Mb
Release : 2013-12-19
Category : Mathematics
ISBN : 9783662404096

Get Book

Abstract Harmonic Analysis by Edwin Hewitt,Kenneth Allen Ross Pdf

When we accepted the kind invitation of Prof. Dr. F.K. SCHMIDT to write a monograph on abstract harmonie analysis for the Grundlehren der Mathematischen Wissenschaften series, we intended to write aH that we could find out about the subject in a text of about 600 printed pages. We intended that our book should be accessible to beginners, and we hoped to make it useful to specialists as weH. These aims proved to be mutuaHy inconsistent. Hence the present volume comprises only half of the projected work. It gives all of the structure of topologie al groups needed for harmonie analysis as it is known to us; it treats integration on locaHy compact groups in detail; it contains an introduction to the theory of group representations. In the second volume we will treat harmonie analysis on compact groups and locally compact Abelian groups, in considerable detail. The book is based on courses given by E. HEWlTT at the University of Washington and the University of Uppsala, although naturally the material of these courses has been enormously expanded to meet the needs of a formal monograph. Like the other treatments of harmonie analysis that have appeared since 1940, the book is a lineal descendant of A. WEIL'S fundamental treatise (WEIL r 4J) 1. The debt of all workers in the field to WEIL'S work is weH known and enormous.

Harmonic and Applied Analysis

Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate
Harmonic and Applied Analysis Book PDF

Author : Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate
Publisher : Birkhäuser
Page : 256 pages
File Size : 55,8 Mb
Release : 2015-09-12
Category : Mathematics
ISBN : 9783319188638

Get Book

Harmonic and Applied Analysis by Stephan Dahlke,Filippo De Mari,Philipp Grohs,Demetrio Labate Pdf

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.​

Toeplitz Operators and Index Theory in Several Complex Variables

Harald Upmeier
Toeplitz Operators and Index Theory in Several Complex Variables Book PDF

Author : Harald Upmeier
Publisher : Birkhäuser
Page : 495 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034892469

Get Book

Toeplitz Operators and Index Theory in Several Complex Variables by Harald Upmeier Pdf

4. 1 Bergman-Toeplitz Operators Over Bounded Domains 242 4. 2 Hardy-Toeplitz Operators Over Strictly Domains Pseudoconvex 250 Groupoid C* -Algebras 4. 3 256 4. 4 Hardy-Toeplitz Operators Over Tubular Domains 267 4. 5 Bergman-Toeplitz Operators Over Tubular Domains 278 4. 6 Hardy-Toeplitz Operators Over Polycircular Domains 284 4. 7 Bergman-Toeplitz Operators Over Polycircular Domains 290 4. 8 Hopf C* -Algebras 299 4. 9 Actions and Coactions on C* -Algebras 310 4. 10 Hardy-Toeplitz Operators Over K-circular Domains 316 4. 11 Hardy-Toeplitz Operators Over Symmetric Domains 325 4. 12 Bergman-Toeplitz Operators Over Symmetric Domains 361 5. Index Theory for Multivariable Toeplitz Operators 5. 0 Introduction 371 5. 1 K-Theory for Topological Spaces 372 5. 2 Index Theory for Strictly Pseudoconvex Domains 384 5. 3 C*-Algebras K-Theory for 394 5. 4 Index Theory for Symmetric Domains 400 5. 5 Index Theory for Tubular Domains 432 5. 6 Index Theory for Polycircular Domains 455 References 462 Index of Symbols and Notations 471 In trod uction Toeplitz operators on the classical Hardy space (on the I-torus) and the closely related Wiener-Hopf operators (on the half-line) form a central part of operator theory, with many applications e. g. , to function theory on the unit disk and to the theory of integral equations.

Operator Algebras and Quantum Statistical Mechanics 1

Ola Bratteli,Derek William Robinson
Operator Algebras and Quantum Statistical Mechanics 1 Book PDF

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 43,7 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9783662025208

Get Book

Operator Algebras and Quantum Statistical Mechanics 1 by Ola Bratteli,Derek William Robinson Pdf

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

Operator Algebras in Dynamical Systems

Shôichirô Sakai
Operator Algebras in Dynamical Systems Book PDF

Author : Shôichirô Sakai
Publisher : Unknown
Page : 233 pages
File Size : 53,9 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1107088232

Get Book

Operator Algebras in Dynamical Systems by Shôichirô Sakai Pdf

This book is essential reading for graduate students and professionals working in operator algebras, mathematical physics and functional analysis.

Harmonic Analysis on Free Groups

Alessandro Figa-Talamanca
Harmonic Analysis on Free Groups Book PDF

Author : Alessandro Figa-Talamanca
Publisher : CRC Press
Page : 164 pages
File Size : 54,8 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000153293

Get Book

Harmonic Analysis on Free Groups by Alessandro Figa-Talamanca Pdf

This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.

Operator Algebras and Mathematical Physics

Tirthankar Bhattacharyya,Michael A. Dritschel
Operator Algebras and Mathematical Physics Book PDF

Author : Tirthankar Bhattacharyya,Michael A. Dritschel
Publisher : Birkhäuser
Page : 202 pages
File Size : 50,7 Mb
Release : 2015-09-29
Category : Mathematics
ISBN : 9783319181820

Get Book

Operator Algebras and Mathematical Physics by Tirthankar Bhattacharyya,Michael A. Dritschel Pdf

This volume gathers contributions from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Bangalore, India, in December 2013. All articles were written by experts and cover a broad range of original material at the cutting edge of operator theory and its applications. Topics include multivariable operator theory, operator theory on indefinite metric spaces (Krein and Pontryagin spaces) and its applications, spectral theory with applications to differential operators, the geometry of Banach spaces, scattering and time varying linear systems, and wavelets and coherent states.

Harmonic Analysis and Applications

Christopher Heil
Harmonic Analysis and Applications Book PDF

Author : Christopher Heil
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 48,8 Mb
Release : 2007-08-02
Category : Mathematics
ISBN : 9780817645045

Get Book

Harmonic Analysis and Applications by Christopher Heil Pdf

This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.

Trends in Harmonic Analysis and Its Applications

Jens G. Christensen,Susanna Dann,Azita Mayeli,Gestur Ólafsson
Trends in Harmonic Analysis and Its Applications Book PDF

Author : Jens G. Christensen,Susanna Dann,Azita Mayeli,Gestur Ólafsson
Publisher : American Mathematical Soc.
Page : 209 pages
File Size : 46,6 Mb
Release : 2015-10-27
Category : Harmonic analysis
ISBN : 9781470418793

Get Book

Trends in Harmonic Analysis and Its Applications by Jens G. Christensen,Susanna Dann,Azita Mayeli,Gestur Ólafsson Pdf

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Its Applications held March 29-30, 2014, at the University of Maryland, Baltimore County, Baltimore, MD. It provides an in depth look at the many directions taken by experts in Harmonic Analysis and related areas. The papers cover topics such as frame theory, Gabor analysis, interpolation and Besov spaces on compact manifolds, Cuntz-Krieger algebras, reproducing kernel spaces, solenoids, hypergeometric shift operators and analysis on infinite dimensional groups. Expositions are by leading researchers in the field, both young and established. The papers consist of new results or new approaches to solutions, and at the same time provide an introduction into the respective subjects.

Operator Algebras in Dynamical Systems

Shtichirt Sakai
Operator Algebras in Dynamical Systems Book PDF

Author : Shtichirt Sakai
Publisher : Unknown
Page : 233 pages
File Size : 46,6 Mb
Release : 2014-05-18
Category : C*-algebras
ISBN : 1107094453

Get Book

Operator Algebras in Dynamical Systems by Shtichirt Sakai Pdf

This book is essential reading for graduate students and professionals working in operator algebras, mathematical physics and functional analysis.

Harmonic Functions on Groups and Fourier Algebras

Cho-Ho Chu,Anthony To-Ming Lau
Harmonic Functions on Groups and Fourier Algebras Book PDF

Author : Cho-Ho Chu,Anthony To-Ming Lau
Publisher : Springer
Page : 100 pages
File Size : 42,7 Mb
Release : 2004-10-11
Category : Mathematics
ISBN : 9783540477938

Get Book

Harmonic Functions on Groups and Fourier Algebras by Cho-Ho Chu,Anthony To-Ming Lau Pdf

This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.