# Group Representations Ergodic Theory Operator Algebras And Mathematical Physics

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## Group Representations Ergodic Theory Operator Algebras and Mathematical Physics

Author | : Calvin C. Moore |

Publsiher | : Springer Science & Business Media |

Total Pages | : 278 |

Release | : 2012-12-06 |

ISBN | : 1461247225 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Group Representations Ergodic Theory Operator Algebras and Mathematical Physics Book Excerpt:**

The Mathematical Sciences Research Institute sponsored a three day conference, May 21-23, 1984 to honor Professor George W. Mackey. The title of the conference, Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics, reflects the interests in science that have characterized Professor wide ranging Mackey's work. The conference provided an opportunity for his students, friends and colleagues to honor him and his contributions. The conference was attended by over one hundred people and the participants included five mathematical generations Professor Mackey's mathematical father, Marshall Stone, many mathematical children, grandchildren, and at least one mathematical great-grandchild. This volume is a compendium of the scientific papers presented at the conference plus some additional papers contributed after the conference. The far ranging scope of the various articles is a further indication of the large number of fields that have been affected by Professor Mackey's work. Calvin C. Moore Berkeley, CA Feb, 1986 Table of Contents Preface vi i Ambiguity Functions and Group L. Auslander and Representations R. Tolimieri Kirillov Orbits and Direct Integral Lawrence Corwin 11 Decompositions on Certain Quotient Spaces Some Homotopy and Shape Calculations Edward G. Effors and 69 for C*-Algebras Jerome Kaminker 121 Small Unitary Representations of Roger Howe Classical Groups Dual Vector Spaces Irving Kaplansky 151 Exponential Decay of Correlation Calvin C. Moore 163 Coefficients for Geodesic Flows Lattices in U(n. I) G. D. Mostow Induced Bundles and Nonlinear Irving E. Segal 199 Wave equations Compact Ahelian Aut.

## Group Representations Ergodic Theory Operator Algebras and Mathematical Physics

Author | : Calvin C Moore |

Publsiher | : Unknown |

Total Pages | : 292 |

Release | : 1986-12-22 |

ISBN | : 9781461247234 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Group Representations Ergodic Theory Operator Algebras and Mathematical Physics Book Excerpt:**

## Group Representations Ergodic Theory and Mathematical Physics

Author | : Robert S. Doran,Calvin C. Moore,Robert J. Zimmer |

Publsiher | : American Mathematical Soc. |

Total Pages | : 446 |

Release | : 2008 |

ISBN | : 0821842250 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Group Representations Ergodic Theory and Mathematical Physics Book Excerpt:**

George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics. Topics examined here include recent results on induced representations, virtual groups, the Mackey Machine and crossed products, representations of Baumslag-Solitar groups, the Radon transform and the heat equation, groupoids in the study of wavelets, and quantum theory. The in-depth historical surveys of Mackey's work on representation theory, ergodic theory, and physics, together with recent developments inspired by his fundamental work will be of considerable interest to both graduate students and researchers alike.

## Group Representations Ergodic Theory Operator Algebras and Mathematical Physics

Author | : Calvin C. Moore |

Publsiher | : Unknown |

Total Pages | : 278 |

Release | : 1987 |

ISBN | : 9783540964711 |

Category | : Algèbres d'opérateurs - Congrès |

Language | : EN, FR, DE, ES & NL |

**Group Representations Ergodic Theory Operator Algebras and Mathematical Physics Book Excerpt:**

## Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces

Author | : M. Bachir Bekka,Mohammed El Bachir Bekka,Matthias Mayer |

Publsiher | : Cambridge University Press |

Total Pages | : 200 |

Release | : 2000-05-11 |

ISBN | : 9780521660303 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces Book Excerpt:**

This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.

## Group Actions in Ergodic Theory Geometry and Topology

Author | : Robert J. Zimmer |

Publsiher | : University of Chicago Press |

Total Pages | : 608 |

Release | : 2019-12-23 |

ISBN | : 022656827X |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Group Actions in Ergodic Theory Geometry and Topology Book Excerpt:**

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.

## Dynamical Systems Ergodic Theory and Applications

Author | : L.A. Bunimovich,S.G. Dani,R.L. Dobrushin,M.V. Jakobson,I.P. Kornfeld,N.B. Maslova,Ya.B. Pesin,J. Smillie,Yu.M. Sukhov,A.M. Vershik |

Publsiher | : Springer Science & Business Media |

Total Pages | : 460 |

Release | : 2000-04-05 |

ISBN | : 9783540663164 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Dynamical Systems Ergodic Theory and Applications Book Excerpt:**

This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

## Ergodic Theory Groups and Geometry

Author | : Robert J. Zimmer,Dave Witte Morris |

Publsiher | : American Mathematical Soc. |

Total Pages | : 87 |

Release | : 2008 |

ISBN | : 0821809806 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ergodic Theory Groups and Geometry Book Excerpt:**

This introduction to ergodic theory provides an overview of important methods, major developments and open problems in the subject. The lectures in the book include additional comments at the end of each chapter with references to recent developments. These updates can help lead the graduate student to cutting-edge results in the field.

## Geometry and Physics Volume 2

Author | : Jørgen Ellegaard Andersen,Andrew Dancer,Oscar García-Prada |

Publsiher | : Oxford University Press |

Total Pages | : 400 |

Release | : 2018-10-18 |

ISBN | : 019252237X |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Geometry and Physics Volume 2 Book Excerpt:**

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997. Geometry and Physics: A Festschrift in honour of Nigel Hitchin contain the proceedings of the conferences held in September 2016 in Aarhus, Oxford, and Madrid to mark Nigel Hitchin's 70th birthday, and to honour his far-reaching contributions to geometry and mathematical physics. These texts contain 29 articles by contributors to the conference and other distinguished mathematicians working in related areas, including three Fields Medallists. The articles cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics.

## Geometry and Physics Volume 2

Author | : Andrew Dancer,Jørgen Ellegaard Andersen,Oscar García-Prada |

Publsiher | : Unknown |

Total Pages | : 352 |

Release | : 2018-10-25 |

ISBN | : 0198802021 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Geometry and Physics Volume 2 Book Excerpt:**

These texts contain 29 articles that cover a broad range of topics in differential, algebraic and symplectic geometry, and also in mathematical physics. These volumes will be of interest to researchers and graduate students in geometry and mathematical physics

## K Theory for Operator Algebras

Author | : Bruce Blackadar |

Publsiher | : Cambridge University Press |

Total Pages | : 300 |

Release | : 1998-09-13 |

ISBN | : 9780521635325 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**K Theory for Operator Algebras Book Excerpt:**

This book is the only comprehensive treatment of K-theory for operator algebras.

## Representation Theory of Lie Groups

Author | : Jeffrey Adams, David Vogan |

Publsiher | : American Mathematical Soc. |

Total Pages | : 340 |

Release | : 2015-06-02 |

ISBN | : 1470423146 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Representation Theory of Lie Groups Book Excerpt:**

This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups. The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the year 1975, specifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the Langlands classification. Additional contributions outline developments in four of the most active areas of research over the past 20 years. The clearly written articles present results to date, as follows: R. Zierau and L. Barchini discuss the construction of representations on Dolbeault cohomology spaces. D. Vogan describes the status of the Kirillov-Kostant "philosophy of coadjoint orbits" for unitary representations. K. Vilonen presents recent advances in the Beilinson-Bernstein theory of "localization". And Jian-Shu Li covers Howe's theory of "dual reductive pairs". Each contributor to the volume presents the topics in a unique, comprehensive, and accessible manner geared toward advanced graduate students and researchers. Students should have completed the standard introductory graduate courses for full comprehension of the work. The book would also serve well as a supplementary text for a course on introductory infinite-dimensional representation theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

## Handbook of Dynamical Systems

Author | : B. Hasselblatt,A. Katok |

Publsiher | : Elsevier |

Total Pages | : 1232 |

Release | : 2002-08-20 |

ISBN | : 0080533442 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Handbook of Dynamical Systems Book Excerpt:**

Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005.

## Smooth Ergodic Theory and Its Applications

Author | : AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications,Ams Summer Research Institute on Smooth Ergodic Theory and Its Applications (1999 Univer |

Publsiher | : American Mathematical Soc. |

Total Pages | : 881 |

Release | : 2001 |

ISBN | : 0821826824 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Smooth Ergodic Theory and Its Applications Book Excerpt:**

During the past decade, there have been several major new developments in smooth ergodic theory, which have attracted substantial interest to the field from mathematicians as well as scientists using dynamics in their work. In spite of the impressive literature, it has been extremely difficult for a student - or even an established mathematician who is not an expert in the area - to acquire a working knowledge of smooth ergodic theory and to learn how to use its tools.Accordingly, the AMS Summer Research Institute on Smooth Ergodic Theory and Its Applications (Seattle, WA) had a strong educational component, including ten mini-courses on various aspects of the topic that were presented by leading experts in the field. This volume presents the proceedings of that conference. Smooth ergodic theory studies the statistical properties of differentiable dynamical systems, whose origin traces back to the seminal works of Poincare and later, many great mathematicians who made contributions to the development of the theory.The main topic of this volume, smooth ergodic theory, especially the theory of nonuniformly hyperbolic systems, provides the principle paradigm for the rigorous study of complicated or chaotic behavior in deterministic systems. This paradigm asserts that if a non-linear dynamical system exhibits sufficiently pronounced exponential behavior, then global properties of the system can be deduced from studying the linearized system. One can then obtain detailed information on topological properties (such as the growth of periodic orbits, topological entropy, and dimension of invariant sets including attractors), as well as statistical properties (such as the existence of invariant measures, asymptotic behavior of typical orbits, ergodicity, mixing, decay of correlations, and measure-theoretic entropy).Smooth ergodic theory also provides a foundation for numerous applications throughout mathematics (e.g., Riemannian geometry, number theory, Lie groups, and partial differential equations), as well as other sciences. This volume serves a two-fold purpose: first, it gives a useful gateway to smooth ergodic theory for students and nonspecialists, and second, it provides a state-of-the-art report on important current aspects of the subject. The book is divided into three parts: lecture notes consisting of three long expositions with proofs aimed to serve as a comprehensive and self-contained introduction to a particular area of smooth ergodic theory; thematic sections based on mini-courses or surveys held at the conference; and original contributions presented at the meeting or closely related to the topics that were discussed there.

## Group Representations Ergodic Theory and Mathematical Physics

Author | : Robert S. Doran,Calvin C. Moore,Robert J. Zimmer |

Publsiher | : American Mathematical Soc. |

Total Pages | : 446 |

Release | : 2008-01-17 |

ISBN | : 9780821857786 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Group Representations Ergodic Theory and Mathematical Physics Book Excerpt:**

George Mackey was an extraordinary mathematician of great power and vision. His profound contributions to representation theory, harmonic analysis, ergodic theory, and mathematical physics left a rich legacy for researchers that continues today. This book is based on lectures presented at an AMS special session held in January 2007 in New Orleans dedicated to his memory. The papers, written especially for this volume by internationally-known mathematicians and mathematical physicists, range from expository and historical surveys to original high-level research articles. The influence of Mackey's fundamental ideas is apparent throughout. The introductory article contains recollections from former students, friends, colleagues, and family as well as a biography describing his distinguished career as a mathematician at Harvard, where he held the Landon D. Clay Professorship of Mathematics. Topics examined here include recent results on induced representations, virtual groups, the Mackey Machine and crossed products, representations of Baumslag-Solitar groups, the Radon transform and the heat equation, groupoids in the study of wavelets, and quantum theory. The in-depth historical surveys of Mackey's work on representation theory, ergodic theory, and physics, together with recent developments inspired by his fundamental work will be of considerable interest to both graduate students and researchers alike.

## Ergodic Theory and Harmonic Analysis

Author | : London Mathematical Society |

Publsiher | : Cambridge University Press |

Total Pages | : 437 |

Release | : 1995-01-27 |

ISBN | : 0521459990 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Ergodic Theory and Harmonic Analysis Book Excerpt:**

Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence, rigidity theory and the theory of joinings. These papers present the background of each area of interaction, the most outstanding results and promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. Thirteen related research papers describe the work; several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder deal with convergence and a variety of other topics in dynamics.

## A Window Into Zeta and Modular Physics

Author | : Klaus Kirsten,Floyd L. Williams |

Publsiher | : Cambridge University Press |

Total Pages | : 351 |

Release | : 2010-05-24 |

ISBN | : 0521199301 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**A Window Into Zeta and Modular Physics Book Excerpt:**

"A book consisting of lectures that are part of the series of MSRI workshops and that introduce students and researchers to a portion of the intriguing world of theoretical physics"--

## Representations of Nilpotent Lie Groups and Their Applications Volume 1 Part 1 Basic Theory and Examples

Author | : Laurence Corwin,Frederick P. Greenleaf |

Publsiher | : Cambridge University Press |

Total Pages | : 269 |

Release | : 1990-08-30 |

ISBN | : 9780521604956 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Representations of Nilpotent Lie Groups and Their Applications Volume 1 Part 1 Basic Theory and Examples Book Excerpt:**

The first exposition of group representations and harmonic analysis for graduates for over twenty years.

## Operator Algebra and Dynamics

Author | : Toke M. Carlsen,Søren Eilers,Gunnar Restorff,Sergei Silvestrov |

Publsiher | : Springer Science & Business Media |

Total Pages | : 332 |

Release | : 2013-12-03 |

ISBN | : 3642394590 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Operator Algebra and Dynamics Book Excerpt:**

Based on presentations given at the NordForsk Network Closing Conference “Operator Algebra and Dynamics,” held in Gjáargarður, Faroe Islands, in May 2012, this book features high quality research contributions and review articles by researchers associated with the NordForsk network and leading experts that explore the fundamental role of operator algebras and dynamical systems in mathematics with possible applications to physics, engineering and computer science. It covers the following topics: von Neumann algebras arising from discrete measured groupoids, purely infinite Cuntz-Krieger algebras, filtered K-theory over finite topological spaces, C*-algebras associated to shift spaces (or subshifts), graph C*-algebras, irrational extended rotation algebras that are shown to be C*-alloys, free probability, renewal systems, the Grothendieck Theorem for jointly completely bounded bilinear forms on C*-algebras, Cuntz-Li algebras associated with the a-adic numbers, crossed products of injective endomorphisms (the so-called Stacey crossed products), the interplay between dynamical systems, operator algebras and wavelets on fractals, C*-completions of the Hecke algebra of a Hecke pair, semiprojective C*-algebras, and the topological dimension of type I C*-algebras. Operator Algebra and Dynamics will serve as a useful resource for a broad spectrum of researchers and students in mathematics, physics, and engineering.

## Rigidity in Higher Rank Abelian Group Actions Volume 1 Introduction and Cocycle Problem

Author | : Anatole Katok,Viorel Niţică |

Publsiher | : Cambridge University Press |

Total Pages | : 313 |

Release | : 2011-06-16 |

ISBN | : 1139496867 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Rigidity in Higher Rank Abelian Group Actions Volume 1 Introduction and Cocycle Problem Book Excerpt:**

This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.