Rearrangement of Coefficients of Fourier Series on SU2 PDF Download
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Author: Giancarlo Travaglini
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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Author: Giancarlo Travaglini
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
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Book Description
Author: Tyler Leaser
Publisher:
ISBN:
Category : Fourier analysis
Languages : en
Pages : 125
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Book Description
The set SU(2) of 2x2 unitary matrices with determinant one forms a compact non-abelian Lie group diffeomorphic to the three dimensional sphere. This thesis surveys general theory concerning analysis on compact Lie groups and applies this in the setting of SU(2). Our principal reference is J. Faraut's book {\em Analysis on Lie Groups}. Fundamental results in representation theory with compact Lie groups include the Peter-Weyl Theorem, Plancherel Theorem and a criterion for uniform convergence of Fourier series. On SU(2) we give explicit constructions for Haar measure and all irreducible unitary representations. For purposes of motivation and comparison we also consider analysis on U(1), the unit circle in the complex plane. In this context, the general theory specializes to yield classical results on Fourier series with periodic functions and the heat equation in one dimension. We discuss convergence behavior of Fourier series on SU(2) and show that Cauchy problem for the heat equation with continuous boundary data admits a unique solution.
Author: M. Sugiura
Publisher: Elsevier
ISBN: 0080887597
Category : Mathematics
Languages : en
Pages : 469
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Book Description
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: Roelof W. Bruggeman
Publisher: Springer Nature
ISBN: 3031431928
Category : Mathematics
Languages : en
Pages : 217
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Book Description
This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.
Author: Dennis M. Healy
Publisher:
ISBN:
Category : Compact spaces
Languages : en
Pages : 286
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Book Description
Author: Russell L. Herman
Publisher: CRC Press
ISBN: 1498773729
Category : Mathematics
Languages : en
Pages : 541
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Book Description
This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering. This introductory textbook was written with mathematics, science, and engineering students with a background in calculus and basic linear algebra in mind. It can be used as a textbook for undergraduate courses in Fourier analysis or applied mathematics, which cover Fourier series, orthogonal functions, Fourier and Laplace transforms, and an introduction to complex variables. These topics are tied together by the application of the spectral analysis of analog and discrete signals, and provide an introduction to the discrete Fourier transform. A number of examples and exercises are provided including implementations of Maple, MATLAB, and Python for computing series expansions and transforms. After reading this book, students will be familiar with: • Convergence and summation of infinite series • Representation of functions by infinite series • Trigonometric and Generalized Fourier series • Legendre, Bessel, gamma, and delta functions • Complex numbers and functions • Analytic functions and integration in the complex plane • Fourier and Laplace transforms. • The relationship between analog and digital signals Dr. Russell L. Herman is a professor of Mathematics and Professor of Physics at the University of North Carolina Wilmington. A recipient of several teaching awards, he has taught introductory through graduate courses in several areas including applied mathematics, partial differential equations, mathematical physics, quantum theory, optics, cosmology, and general relativity. His research interests include topics in nonlinear wave equations, soliton perturbation theory, fluid dynamics, relativity, chaos and dynamical systems.
Author: Anders Vretblad
Publisher: Springer Science & Business Media
ISBN: 0387217231
Category : Mathematics
Languages : en
Pages : 275
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Book Description
A carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.
Author: Stephen S. Gelbart
Publisher: American Mathematical Soc.
ISBN:
Category : Fourier analysis
Languages : en
Pages : 84
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Book Description
Author: Gregory S. Chirikjian
Publisher: Courier Dover Publications
ISBN: 0486795640
Category : Mathematics
Languages : en
Pages : 881
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Book Description
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: Jayakumar Ramanathan
Publisher: Springer Science & Business Media
ISBN: 1461217563
Category : Mathematics
Languages : en
Pages : 334
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Book Description
