Unitary Representations of Locally Compact Groups- PDF Download

Author: Louis Auslander
Publisher:
ISBN:
Category : Continuous groups
Languages : en
Pages : 392

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Author: Eberhard Kaniuth
Publisher: Cambridge University Press
ISBN: 052176226X
Category : Mathematics
Languages : en
Pages : 359

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Book Description
A comprehensive presentation of the theories of induced representations and Mackey analysis applied to a wide variety of groups.

Author: J. M.G. Fell
Publisher: Academic Press
ISBN: 9780080874449
Category : Mathematics
Languages : en
Pages : 746

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Book Description
This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.

Author: Alain Robert
Publisher: Cambridge University Press
ISBN: 0521289750
Category : Mathematics
Languages : en
Pages : 217

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Book Description
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.

Author: Edwin Hewitt
Publisher: Springer Science & Business Media
ISBN: 9783540583189
Category : Mathematics
Languages : en
Pages : 786

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Book Description
Vol. I. Structure of topological groups, intégration theory group représentations. Vol. II, Structure and analysis for compact groups, Analysis on locally compact abelian groups.

Author: Gerald B. Folland
Publisher: CRC Press
ISBN: 1498727158
Category : Mathematics
Languages : en
Pages : 317

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Book Description
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

Author: J. M.G. Fell
Publisher: Academic Press
ISBN: 9780080874456
Category : Mathematics
Languages : en
Pages : 752

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Book Description
This is an all-encompassing and exhaustive exposition of the theory of infinite-dimensional Unitary Representations of Locally Compact Groups and its generalization to representations of Banach algebras. The presentation is detailed, accessible, and self-contained (except for some elementary knowledge in algebra, topology, and abstract measure theory). In the later chapters the reader is brought to the frontiers of present-day knowledge in the area of Mackey normal subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.

Author: Bachir Bekka
Publisher: American Mathematical Soc.
ISBN: 1470456273
Category : Education
Languages : en
Pages : 489

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Book Description
Unitary representations of groups play an important role in many subjects, including number theory, geometry, probability theory, partial differential equations, and quantum mechanics. This monograph focuses on dual spaces associated to a group, which are spaces of building blocks of general unitary representations. Special attention is paid to discrete groups for which the unitary dual, the most common dual space, has proven to be not useful in general and for which other duals spaces have to be considered, such as the primitive dual, the normal quasi-dual, or spaces of characters. The book offers a detailed exposition of these alternative dual spaces and covers the basic facts about unitary representations and operator algebras needed for their study. Complete and elementary proofs are provided for most of the fundamental results that up to now have been accessible only in original papers and appear here for the first time in textbook form. A special feature of this monograph is that the theory is systematically illustrated by a family of examples of discrete groups for which the various dual spaces are discussed in great detail: infinite dihedral group, Heisenberg groups, affine groups of fields, solvable Baumslag-Solitar group, lamplighter group, and general and special linear groups. The book will appeal to graduate students who wish to learn the basics facts of an important topic and provides a useful resource for researchers from a variety of areas. The only prerequisites are a basic background in group theory, measure theory, and operator algebras.

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 0817644423
Category : Mathematics
Languages : en
Pages : 466

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Book Description
* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician

Author: Anthony W. Knapp
Publisher: Princeton University Press
ISBN: 1400883938
Category : Mathematics
Languages : en
Pages : 968

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Book Description
This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced by Zuckerman, is an algebraic analog that is technically more manageable than the complex-analysis construction and leads to a large repertory of irreducible unitary representations of reductive Lie groups. The book, which is accessible to students beyond the first year of graduate school, will interest mathematicians and physicists who want to learn about and take advantage of the algebraic side of the representation theory of Lie groups. Cohomological Induction and Unitary Representations develops the necessary background in representation theory and includes an introductory chapter of motivation, a thorough treatment of the "translation principle," and four appendices on algebra and analysis.