Introduction to the Representation Theory of Compact and Locally Compact Groups
Introduction to the Representation Theory of Compact and Locally Compact Groups

Author: Alain Robert

Publisher: Cambridge University Press

Published: 1983-02-10

Total Pages: 217

ISBN-13: 0521289750

DOWNLOAD EBOOK

Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.

A Course in Abstract Harmonic Analysis
A Course in Abstract Harmonic Analysis

Author: Gerald B. Folland

Publisher: CRC Press

Published: 2016-02-03

Total Pages: 317

ISBN-13: 1498727158

DOWNLOAD EBOOK

A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul

Introduction to the Theory of Banach Representations of Groups
Introduction to the Theory of Banach Representations of Groups

Author: Yurii I. Lyubich

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 231

ISBN-13: 3034891695

DOWNLOAD EBOOK

The theory of group representations plays an important roie in modern mathematics and its applica~ions to natural sciences. In the compulsory university curriculum it is included as a branch of algebra, dealing with representations of finite groups (see, for example, the textbook of A. I. Kostrikin [25]). The representation theory for compact, locally compact Abelian, and Lie groups is co vered in graduate courses, concentrated around functional analysis. The author of the present boo~ has lectured for many years on functional analysis at Khar'kov University. He subsequently con tinued these lectures in the form of a graduate course on the theory of group representations, in which special attention was devoted to a retrospective exposition of operator theory and harmo nic analysis of functions from the standpoint of representation theory. In this approach it was natural to consider not only uni tary, but also Banach representations, and not only representations of groups, but also of semigroups.

Lie Algebras and Locally Compact Groups
Lie Algebras and Locally Compact Groups

Author: Irving Kaplansky

Publisher: University of Chicago Press

Published: 1971

Total Pages: 161

ISBN-13: 0226424537

DOWNLOAD EBOOK

This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups," deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.

Representations of Compact Lie Groups
Representations of Compact Lie Groups

Author: T. Bröcker

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 323

ISBN-13: 3662129183

DOWNLOAD EBOOK

This introduction to the representation theory of compact Lie groups follows Herman Weyl’s original approach. It discusses all aspects of finite-dimensional Lie theory, consistently emphasizing the groups themselves. Thus, the presentation is more geometric and analytic than algebraic. It is a useful reference and a source of explicit computations. Each section contains a range of exercises, and 24 figures help illustrate geometric concepts.

Probability on Compact Lie Groups
Probability on Compact Lie Groups

Author: David Applebaum

Publisher: Springer

Published: 2014-06-26

Total Pages: 236

ISBN-13: 3319078429

DOWNLOAD EBOOK

Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.

Pontryagin Duality and the Structure of Locally Compact Abelian Groups
Pontryagin Duality and the Structure of Locally Compact Abelian Groups

Author: Sidney A. Morris

Publisher: Cambridge University Press

Published: 1977-08-04

Total Pages: 141

ISBN-13: 0521215439

DOWNLOAD EBOOK

These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.