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    The eight songs on this playlist didn't "inspire" The Buried Giant, nor did I play them out loud while writing. And with the notable exception of... Continue »
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      The Buried Giant

      Kazuo Ishiguro 9780307271037

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25 Remote Warehouse Mathematics- Analysis General

Fourier Analysis on Finite Abelian Groups (Applied and Numerical Harmonic Analysis)

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Fourier Analysis on Finite Abelian Groups (Applied and Numerical Harmonic Analysis) Cover

 

Synopses & Reviews

Publisher Comments:

Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, cryptography, algorithms, and sequence design. This self-contained book provides a thorough look at the Fourier transform, one of the most useful tools in applied mathematics. With countless examples and unique exercise sets at the end of most sections, Fourier Analysis on Finite Abelian Groups is a perfect companion for a first course in Fourier analysis. The first two chapters provide fundamental material for a strong foundation to deal with subsequent chapters. Special topics covered include: * Computing eigenvalues of the Fourier transform * Applications to Banach algebras * Tensor decompositions of the Fourier transform * Quadratic Gaussian sums This book provides a useful introduction for well-prepared undergraduate and graduate students and powerful applications that may appeal to researchers and mathematicians. The only prerequisites are courses in group theory and linear algebra.

Synopsis:

This self-contained overview examines the decomposition and analysis of functions within Fourier transforms and Abelian groups. Readers will learn the fundamentals, which are illustrated by examples and unique exercises at the end of each section.

Synopsis:

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.

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.

Product Details

ISBN:
9780817649159
Author:
Luong, Bao
Publisher:
Birkhauser
Location:
Boston, MA
Subject:
Mathematical Analysis
Subject:
Group Theory
Subject:
Algebra - Abstract
Subject:
Mathematics-Analysis General
Subject:
Banach algebras
Subject:
Chebyshev systems
Subject:
Fourier transform
Subject:
Gaussian sums.
Subject:
finite abelian groups
Subject:
quadratic Gaussian sums
Subject:
tensor decomposition
Subject:
Vector spaces
Subject:
Fourier analysis
Subject:
Group Theory and Generalizations
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Description:
2009
Series:
Applied and Numerical Harmonic Analysis
Publication Date:
20090826
Binding:
HARDCOVER
Language:
English
Pages:
175
Dimensions:
235 x 155 mm 940 gr

Related Subjects

Science and Mathematics » Mathematics » Algebra » Abstract Algebra
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Group Theory

Fourier Analysis on Finite Abelian Groups (Applied and Numerical Harmonic Analysis) New Hardcover
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$77.50 In Stock
Product details 175 pages Birkhauser Boston - English 9780817649159 Reviews:
"Synopsis" by , This self-contained overview examines the decomposition and analysis of functions within Fourier transforms and Abelian groups. Readers will learn the fundamentals, which are illustrated by examples and unique exercises at the end of each section.
"Synopsis" by , 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.
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