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Author : Werner Ruhl,Werner Rühl
Publisher : Unknown
Page : 326 pages
File Size : 45,7 Mb
Release : 1970
Category : Mathematics
ISBN : UVA:X001450474
Author : V. K. Dobrev,G. Mack,V. B. Petkova
Publisher : Unknown
Page : 298 pages
File Size : 54,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662195763
Author : V. K. Dobrev
Publisher : Springer
Page : 280 pages
File Size : 49,5 Mb
Release : 1977-01-01
Category : Analyse harmonique
ISBN : 038708150X
Author : Moshe Carmeli
Publisher : World Scientific
Page : 416 pages
File Size : 45,6 Mb
Release : 2000
Category : Science
ISBN : 1860942342
This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory. There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -- particularly the Lorentz and the SL(2, C) groups -- to the theory of general relativity. Each chapter is concluded with a set of problems. The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2, C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed. The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.
Author : Pavel Winternitz
Publisher : Unknown
Page : 216 pages
File Size : 48,6 Mb
Release : 1973
Category : Harmonic analysis
ISBN : OCLC:1152231
Author : Charles V. Benton
Publisher : Nova Publishers
Page : 286 pages
File Size : 47,9 Mb
Release : 2004
Category : Mathematics
ISBN : 1590339398
Physics and mathematics have always been closely intertwined, with developments in one field frequently inspiring the other. Currently, there are many unsolved problems in physics which will likely require innovations in mathematical physics. Mathematical physics is concerned with problems in statistical mechanics, atomic and molecular physics, quantum field theory, and, in general, with the mathematical foundations of theoretical physics. mechanics (both nonrelativistic and relativistic), atomic and molecular physics, the existence and properties of the phases of model ferromagnets, the stability of matter, the theory of symmetry and symmetry breaking in quantum field theory (both in general and in concrete models), and mathematical developments in functional analysis and algebra to which such subjects lead. This book presents leading-edge research in this fast-moving field. Structure of the Kalb-Ramond Gauge Symmetry and Spinor Representations; Group Theoretical Interpretation of CPT-Theorem; Cross Recurrence Plots and Their Applications; Analytical Solutions of the Radiative Transfer Equation in One-dimensional Spherical Geometry With Central Symmetry; Hyperspherical Functions and Harmonic Analysis on the Lorentz Group; The Next Stage: Quantum Game Theory; Index.
Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : CRC Press
Page : 555 pages
File Size : 52,6 Mb
Release : 2021-02-25
Category : Mathematics
ISBN : 9781000697339
First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.
Author : Gregory S. Chirikjian,Alexander B. Kyatkin
Publisher : Courier Dover Publications
Page : 881 pages
File Size : 40,7 Mb
Release : 2016-07-20
Category : Mathematics
ISBN : 9780486795645
Although the Fourier transform is among engineering's most widely used mathematical tools, few engineers realize that the extension of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. This self-contained approach, geared toward readers with a standard background in engineering mathematics, explores the widest possible range of applications to fields such as robotics, mechanics, tomography, sensor calibration, estimation and control, liquid crystal analysis, and conformational statistics of macromolecules. Harmonic analysis is explored in terms of particular Lie groups, and the text deals with only a limited number of proofs, focusing instead on specific applications and fundamental mathematical results. Forming a bridge between pure mathematics and the challenges of modern engineering, this updated and expanded volume offers a concrete, accessible treatment that places the general theory in the context of specific groups.
Author : Alessandro Figa-Talamanca
Publisher : CRC Press
Page : 160 pages
File Size : 46,8 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781000116748
This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.
Author : Garth Warner
Publisher : Springer Science & Business Media
Page : 545 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642502750
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 : Michael Eugene Taylor
Publisher : American Mathematical Soc.
Page : 328 pages
File Size : 49,7 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821815236
This book explores some basic roles of Lie groups in linear analysis, with particular emphasis on the generalizations of the Fourier transform and the study of partial differential equations. It began as lecture notes for a one-semester graduate course given by the author in noncommutative harmonic analysis. It is a valuable resource for both graduate students and faculty, and requires only a background with Fourier analysis and basic functional analysis, plus the first few chapters of a standard text on Lie groups. The basic method of noncommutative harmonic analysis, a generalization of Fourier analysis, is to synthesize operators on a space on which a Lie group has a unitary representation from operators on irreducible representation spaces.Though the general study is far from complete, this book covers a great deal of the progress that has been made on important classes of Lie groups. Unlike many other books on harmonic analysis, this book focuses on the relationship between harmonic analysis and partial differential equations. The author considers many classical PDEs, particularly boundary value problems for domains with simple shapes, that exhibit noncommutative groups of symmetries. Also, the book contains detailed work, which has not previously been published, on the harmonic analysis of the Heisenberg group and harmonic analysis on cones.
Author : V. S. Varadarajan
Publisher : Cambridge University Press
Page : 326 pages
File Size : 45,9 Mb
Release : 1999-07-22
Category : Mathematics
ISBN : 0521663628
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 : M. Sugiura
Publisher : Elsevier
Page : 451 pages
File Size : 54,5 Mb
Release : 1990-03-01
Category : Mathematics
ISBN : 0080887597
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 : A.A. Kirillov
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 54,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662097564
Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.
Author : Moshe Carmeli
Publisher : World Scientific
Page : 412 pages
File Size : 45,5 Mb
Release : 2000-11-15
Category : Science
ISBN : 9781783261697
This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory.There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups -particularly the Lorentz and the SL(2,C) groups — to the theory of general relativity. Each chapter is concluded with a set of problems.The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2,C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book. The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed.The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.
