Discrete Harmonic Analysis(English, Hardcover, Ceccherini-Silberstein Tullio)

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Discrete Harmonic Analysis(English, Hardcover, Ceccherini-Silberstein Tullio) is written by Ceccherini-Silberstein Tullio and published by Cambridge University Press. It's available with International Standard Book Number or ISBN identification 1107182336 (ISBN 10) and 9781107182332 (ISBN 13).

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.