Fourier Analysis on Finite Abelian Groups

Luong, Bao

ISBN 10: 0817649158 / ISBN 13: 9780817649159

Editore: Birkhauser Boston Inc, 2009

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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. Series: Applied and Numerical Harmonic Analysis. Num Pages: 159 pages, 2 black & white tables, biography. BIC Classification: PBF; PBK. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 11. Weight in Grams: 940. . 2009. Hardback. . . . .

Codice articolo V9780817649159

Dati bibliografici

• Titolo: Fourier Analysis on Finite Abelian Groups
• Editore: Birkhauser Boston Inc
• Data di pubblicazione: 2009
• Lingua: Inglese
• ISBN 10: 0817649158
• ISBN 13: 9780817649159
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, algorithms and sequence design. 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. The first chapter provides the fundamental material that is a strong foundation for all subsequent chapters.

Special topics including:

* Computing Eigenvalues of the Fourier transform

* Applications to Banach algebras

* Tensor decompositions of the Fourier transform

* Quadratic Gaussian sums.

This book 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.

Dalla quarta di copertina

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.