An Introduction To Harmonic Analysis On Semisimple Lie Groups

Author : V. S. Varadarajan
Publisher : Cambridge University Press
Page : 326 pages
File Size : 48,8 Mb
Release : 1999-07-22
Category : Mathematics
ISBN : 0521663628

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An Introduction to Harmonic Analysis on Semisimple Lie Groups by V. S. Varadarajan Pdf

Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the sunject in the context of special examples, without losing sight of its general flow and structure. The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.

Author : Garth Warner
Publisher : Springer Science & Business Media
Page : 545 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642502750

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Harmonic Analysis on Semi-Simple Lie Groups I by Garth Warner Pdf

The representation theory of locally compact groups has been vig orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra. The chief objective of the present volume and its immediate successor is to provide a reasonably self-contained introduction to Harish-Chandra's theory. Granting cer tain basic prerequisites (cf. infra), we have made an effort to give full details and complete proofs of the theorems on which the theory rests. The structure of this volume and its successor is as follows. Each book is divided into chapters; each chapter is divided into sections; each section into numbers. We then use the decimal system of reference; for example, 1. 3. 2 refers to the second number in the third section of the first chapter. Theorems, Propositions, Lemmas, and Corollaries are listed consecutively throughout any given number. Numbers which are set in fine print may be omitted at a first reading. There are a variety of Exam ples scattered throughout the text; the reader, if he is so inclined, can view them as exercises ad libitum. The Appendices to the text collect certain ancillary results which will be used on and off in the systematic exposi tion; a reference of the form A2.

Author : Paul Sally,David A. Vogan
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 46,5 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821815267

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Representation Theory and Harmonic Analysis on Semisimple Lie Groups by Paul Sally,David A. Vogan Pdf

This book brings together five papers that have been influential in the study of Lie groups. Though published more than 20 years ago, these papers made fundamental contributions that deserve much broader exposure. In addition, the subsequent literature that has subsumed these papers cannot replace the originality and vitality they contain. The editors have provided a brief introduction to each paper, as well as a synopsis of the major developments which have occurred in the area covered by each paper. Included here are the doctoral theses of Arthur, Osborne, and Schmid. Arthur's thesis is closely related to Trombi's paper insofar as both deal with harmonic analysis on real semisimple Lie groups, and, in particular, analysis on the Schwartz space of Harish-Chandra. Arthur's thesis is concerned with the image under the Fourier transform of the Schwartz space of a semisimple Lie group of real rank one, while Trombi's paper provides an expository account of the harmonic analysis associated to the decomposition of the Schwartz space under the regular representation. In his thesis, Osborne extends the Atiyah-Bott fixed point theorem for elliptic complexes to obtain a fixed point formula for complexes that are not elliptic. Schmid proves a generalization of the Borel-Weil theorem concerning an explicit and geometric realization of the irreducible representations of a compact, connected semisimple Lie group. Langlands's fundamental paper provides a classification of irreducible, admissible representations of real reductive Lie groups.

Author : Garth Warner
Publisher : Unknown
Page : 0 pages
File Size : 55,7 Mb
Release : 1972
Category : Harmonic analysis
ISBN : LCCN:70160590

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Harmonic Analysis on Semi-simple Lie Groups by Garth Warner Pdf

Author : Garth Warner
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642516405

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Harmonic Analysis on Semi-Simple Lie Groups II by Garth Warner Pdf

Author : Joseph Albert Wolf,Michel Cahen,Marc de Wilde
Publisher : Unknown
Page : 0 pages
File Size : 47,8 Mb
Release : 1980
Category : Lie groups
ISBN : OCLC:1014520841

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Harmonic Analysis and Representations of Semisimple Lie Groups by Joseph Albert Wolf,Michel Cahen,Marc de Wilde Pdf

Author : J. Carmona,M. Vergne
Publisher : Springer
Page : 562 pages
File Size : 55,6 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540387831

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Non Commutative Harmonic Analysis and Lie Groups by J. Carmona,M. Vergne Pdf

Author : Garth Warner
Publisher : Unknown
Page : 512 pages
File Size : 40,5 Mb
Release : 1972
Category : Mathematics
ISBN : UOM:39015015716551

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Harmonic Analysis on Semi-simple Lie Groups by Garth Warner Pdf

Author : V.S. Varadarajan
Publisher : Springer
Page : 531 pages
File Size : 55,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540374206

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Harmonic Analysis on Real Reductive Groups by V.S. Varadarajan Pdf

Author : M. Sugiura
Publisher : Elsevier
Page : 451 pages
File Size : 51,7 Mb
Release : 1990-03-01
Category : Mathematics
ISBN : 0080887597

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Unitary Representations and Harmonic Analysis by M. Sugiura Pdf

The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681647

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An Introduction to the Uncertainty Principle by Sundaram Thangavelu Pdf

In 1932 Norbert Wiener gave a series of lectures on Fourier analysis at the Univer sity of Cambridge. One result of Wiener's visit to Cambridge was his well-known text The Fourier Integral and Certain of its Applications; another was a paper by G. H. Hardy in the 1933 Journalofthe London Mathematical Society. As Hardy says in the introduction to this paper, This note originates from a remark of Prof. N. Wiener, to the effect that "a f and g [= j] cannot both be very small". ... The theo pair of transforms rems which follow give the most precise interpretation possible ofWiener's remark. Hardy's own statement of his results, lightly paraphrased, is as follows, in which f is an integrable function on the real line and f is its Fourier transform: x 2 m If f and j are both 0 (Ix1e- /2) for large x and some m, then each is a finite linear combination ofHermite functions. In particular, if f and j are x2 x 2 2 2 both O(e- / ), then f = j = Ae- / , where A is a constant; and if one x 2 2 is0(e- / ), then both are null.

Author : Roger E. Howe,Eng Chye Tan
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461392002

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Non-Abelian Harmonic Analysis by Roger E. Howe,Eng Chye Tan Pdf

This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.

Author : Anthony W. Knapp
Publisher : Springer Science & Business Media
Page : 622 pages
File Size : 47,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475724530

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Lie Groups Beyond an Introduction by Anthony W. Knapp Pdf

Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics. A feature of the presentation is that it encourages the reader's comprehension of Lie group theory to evolve from beginner to expert: initial insights make use of actual matrices, while later insights come from such structural features as properties of root systems, or relationships among subgroups, or patterns among different subgroups.

Author : David Gurarie
Publisher : Courier Corporation
Page : 466 pages
File Size : 48,6 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780486462882

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Symmetries and Laplacians by David Gurarie Pdf

Designed as an introduction to harmonic analysis and group representations, this book examines concepts, ideas, results, and techniques related to symmetry groups and Laplacians. Its exposition is based largely on examples and applications of general theory, covering a wide range of topics rather than delving deeply into any particular area. Author David Gurarie, a Professor of Mathematics at Case Western Reserve University, focuses on discrete or continuous geometrical objects and structures, such as regular graphs, lattices, and symmetric Riemannian manifolds. Starting with the basics of representation theory, Professor Gurarie discusses commutative harmonic analysis, representations of compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. Among numerous applications included are integrable hamiltonian systems, geodesic flows on symmetric spaces, and the spectral theory of the Hydrogen atom (Schrodinger operator with Coulomb potential) explicated by its Runge-Lenz symmetry. Three helpful appendixes include supplemental information, and the text concludes with references, a list of frequently used notations, and an index.

Author : Alexander A. Kirillov
Publisher : Cambridge University Press
Page : 237 pages
File Size : 50,7 Mb
Release : 2008-07-31
Category : Mathematics
ISBN : 9780521889698

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An Introduction to Lie Groups and Lie Algebras by Alexander A. Kirillov Pdf

Contemporary introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples