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.

Discrete Harmonic Analysis. Representations, Number Theory, Expanders and the Fourier Transform / Scarabotti, Fabio; Ceccherini-Silbersteim, Tullio; Tolli, Filippo. - STAMPA. - (2018).

### Discrete Harmonic Analysis. Representations, Number Theory, Expanders and the Fourier Transform

#### Abstract

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.
##### Scheda breve Scheda completa
9781107182332
Gruppi, Rappresentazioni, grafi, teoria dei numeri, analisi di Fourieri
03 Monografia::03a Saggio, Trattato Scientifico
Discrete Harmonic Analysis. Representations, Number Theory, Expanders and the Fourier Transform / Scarabotti, Fabio; Ceccherini-Silbersteim, Tullio; Tolli, Filippo. - STAMPA. - (2018).
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11573/1119330`