An Introduction To Harmonic Analysis On Semisimple Lie Groups
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An Introduction To Harmonic Analysis On Semisimple Lie Groups
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Author : V. S. Varadarajan
language : en
Publisher: Cambridge University Press
Release Date : 1999-07-22
An Introduction To Harmonic Analysis On Semisimple Lie Groups written by V. S. Varadarajan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07-22 with Mathematics categories.
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.
Harmonic Analysis On Semi Simple Lie Groups I
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Author : Garth Warner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Harmonic Analysis On Semi Simple Lie Groups I written by Garth Warner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Representation Theory And Harmonic Analysis On Semisimple Lie Groups
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Author : Paul J. Sally (Jr.)
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Representation Theory And Harmonic Analysis On Semisimple Lie Groups written by Paul J. Sally (Jr.) and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
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.
Harmonic Analysis On Semi Simple Lie Groups
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Author : Garth Warner
language : en
Publisher:
Release Date : 1972
Harmonic Analysis On Semi Simple Lie Groups written by Garth Warner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Harmonic analysis categories.
Harmonic Analysis On Semi Simple Lie Groups Ii
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Author : Garth Warner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Harmonic Analysis On Semi Simple Lie Groups Ii written by Garth Warner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Harmonic Analysis And Representations Of Semisimple Lie Groups
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Author : Joseph Albert Wolf
language : en
Publisher:
Release Date : 1980
Harmonic Analysis And Representations Of Semisimple Lie Groups written by Joseph Albert Wolf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Lie groups categories.
An Introduction To The Uncertainty Principle
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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To The Uncertainty Principle written by Sundaram Thangavelu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Harmonic Analysis On Real Reductive Groups
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Author : V.S. Varadarajan
language : en
Publisher: Springer
Release Date : 2006-11-14
Harmonic Analysis On Real Reductive Groups written by V.S. Varadarajan and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Unitary Representations And Harmonic Analysis
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Author : M. Sugiura
language : en
Publisher: Elsevier
Release Date : 1990-03-01
Unitary Representations And Harmonic Analysis written by M. Sugiura and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-03-01 with Mathematics categories.
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.
Symmetries And Laplacians
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Author : David Gurarie
language : en
Publisher: Courier Corporation
Release Date : 2007-12-21
Symmetries And Laplacians written by David Gurarie and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-21 with Mathematics categories.
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.