Discrete Harmonic Analysis: Representations, Number Theory, Expanders, and the Fourier Transform (Cambridge Studies in Advanced Mathematics, Series Number 172)

Editor

Cambridge University Press

Fecha de publicaci�n

2018

Idioma

Ingl�s

ISBN 10

1107182336

ISBN 13

9781107182332

Encuadernaci�n

Encuadernaci�n de tapa dura

Estado

New

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Sinopsis

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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Tullio Ceccherini-Silberstein is Professor of Mathematical Analysis at Universit� del Sannio, Benevento. He is also an Editor of the EMS journal Groups, Geometry, and Dynamics. He has written over 90 research articles on topics ranging from functional and harmonic analysis to group theory, ergodic theory and dynamical systems, and theoretical computer sciences. He has also co-authored four monographs and four proceedings volumes.

Fabio Scarabotti is Professor of Mathematical Analysis at Sapienza Universit� di Roma. He has written over 40 research articles on subjects ranging from harmonic analysis to group theory, combinatorics, ergodic theory and dynamical systems, and theoretical computer science. He has also co-authored three monographs.

Filippo Tolli is Professor of Mathematical Analysis at Universit� Roma Tre, Italy. He has written over 30 research articles ranging from harmonic analysis to group theory, combinatorics, Lie groups, and partial differential equations. He has also co-authored three monographs.

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