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Fourier Analysis on Finite Abelian Groups Bao Luong

Fourier Analysis on Finite Abelian Groups By Bao Luong

Fourier Analysis on Finite Abelian Groups by Bao Luong

Reviews:
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Summary

This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups.

Fourier Analysis on Finite Abelian Groups Summary

Fourier Analysis on Finite Abelian Groups by Bao Luong

This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform to finite Abelian groups. With countless examples and unique exercise sets at the end of each section, Fourier Analysis on Finite Abelian Groups is a perfect companion to a first course in Fourier analysis. This text introduces mathematics students to subjects that are within their reach, but it also has powerful applications that may appeal to advanced researchers and mathematicians. The only prerequisites necessary are group theory, linear algebra, and complex analysis.

Fourier Analysis on Finite Abelian Groups Reviews

From the reviews:

The book under review covers, qua orientation, a pretty broad spectrum ... . The author, Bao Luong, targets well-prepared upper-division students and certain 'outsiders' (scientists and engineers) and has taken pains to make his presentation accessible. ... this compact book is indeed very readable ... . there are fifty-six exercises scattered throughout the text, generally quite sporty. (Michael Berg, The Mathematical Association of America, October, 2009)

The presentation is entirely theoretical ... . What the book does do is cover the Fourier transform (FT) on finite abelian groups, with some emphasis on Gaussian quadratic sums (eigenvalues of the FT) and eigenspaces of the FT operator. There are 56 exercises of varying difficulty spread throughout the book. ... may be helpful for that student's review at the end of the course and for the instructor, mathematicians, and many scientists and engineers. (Colin C. Graham, Mathematical Reviews, Issue 2011 e)

Table of Contents

Preface.- Overview.- Chapter 1: Foundation Material.- Results from Group Theory.- Quadratic Congruences.- Chebyshev Systems of Functions.- Chapter 2: The Fourier Transform.- A Special Class of Linear Operators.- Characters.- The Orthogonal Relations for Characters.- The Fourier Transform.- The Fourier Transform of Periodic Functions.- The Inverse Fourier Transform.- The Inversion Formula.- Matrices of the Fourier Transform.- Iterated Fourier Transform.- Is the Fourier Transform a Self-Adjoint Operator?.- The Convolutions Operator.- Banach Algebra.- The Uncertainty Principle.- The Tensor Decomposition.- The Tensor Decomposition of Vector Spaces.- The Fourier Transform and Isometries.- Reduction to Finite Cyclic Groups.- Symmetric and Antisymmetric Functions.- Eigenvalues and Eigenvectors.- Spectrak Theorem.- Ergodic Theorem.- Multiplicities of Eigenvalues.- The Quantum Fourier Transform.- Chapter 3: Quadratic Sums.- 1. The Number G_n(1).- Reduction Formulas.

Additional information

NPB9780817649159
9780817649159
0817649158
Fourier Analysis on Finite Abelian Groups by Bao Luong
Bao Luong
Applied and Numerical Harmonic Analysis
New
Hardback
Birkhauser Boston Inc
2009-08-26
159
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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Customer Reviews - Fourier Analysis on Finite Abelian Groups