Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

Nonfiction, Science & Nature, Mathematics, Number Theory, Algebra
Cover of the book Discrete Harmonic Analysis by Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli, Cambridge University Press
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Author: Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli ISBN: 9781316863657
Publisher: Cambridge University Press Publication: May 31, 2018
Imprint: Cambridge University Press Language: English
Author: Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli
ISBN: 9781316863657
Publisher: Cambridge University Press
Publication: May 31, 2018
Imprint: Cambridge University Press
Language: English

This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.

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This self-contained book introduces readers to discrete harmonic analysis with an emphasis on the Discrete Fourier Transform and the Fast Fourier Transform on finite groups and finite fields, as well as their noncommutative versions. It also features applications to number theory, graph theory, and representation theory of finite groups. Beginning with elementary material on algebra and number theory, the book then delves into advanced topics from the frontiers of current research, including spectral analysis of the DFT, spectral graph theory and expanders, representation theory of finite groups and multiplicity-free triples, Tao's uncertainty principle for cyclic groups, harmonic analysis on GL(2,Fq), and applications of the Heisenberg group to DFT and FFT. With numerous examples, figures, and over 160 exercises to aid understanding, this book will be a valuable reference for graduate students and researchers in mathematics, engineering, and computer science.

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