Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

AvTullio Ceccherini-Silberstein,Fabio Scarabotti

Inbunden, Engelska, 2018

Del 172 i serien Cambridge Studies in Advanced Mathematics

1 153 kr

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2018-06-21
Mått:155 x 235 x 36 mm
Vikt:960 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Studies in Advanced Mathematics
Antal sidor:586
Förlag:Cambridge University Press
ISBN:9781107182332

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Mer om författaren

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.

Recensioner i media

'Although the roots of harmonic analysis lie in the continuous world, in the last few decades the field has also started to play a fundamental role in the discrete one. This book gives a panoramic view of Discrete Harmonic Analysis - an area that touches many branches of mathematics, such as number theory, spectral theory, groups and their representations, and graphs. The authors open a door for the reader taking him or her on a beautiful tour of classical and modern mathematics All this is done in a self-contained way that prepares the reader for cutting-edge research.' Alex Lubotzky, Hebrew University of Jerusalem

Innehållsförteckning

Part I. Finite Abelian Groups and the DFT: 1. Finite Abelian groups; 2. The Fourier transform on finite Abelian groups; 3. Dirichlet's theorem on primes in arithmetic progressions; 4. Spectral analysis of the DFT and number theory; 5. The fast Fourier transform; Part II. Finite Fields and Their Characters: 6. Finite fields; 7. Character theory of finite fields; Part III. Graphs and Expanders: 8. Graphs and their products; 9. Expanders and Ramanujan graphs; Part IV. Harmonic Analysis of Finite Linear Groups: 10. Representation theory of finite groups; 11. Induced representations and Mackey theory; 12. Fourier analysis on finite affine groups and finite Heisenberg groups; 13. Hecke algebras and multiplicity-free triples; 14. Representation theory of GL(2,Fq).