Discrete harmonic analysis: representations, number theory, expanders, and the fourier transform
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...
Gespeichert in:
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| Weitere beteiligte Personen: | , |
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2018
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
172 |
| Links: | https://doi.org/10.1017/9781316856383 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (xiii, 573 Seiten) |
| ISBN: | 9781316856383 |
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 172 | |
| 520 | |a 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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| spelling | Ceccherini-Silberstein, Tullio Discrete harmonic analysis representations, number theory, expanders, and the fourier transform Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli Cambridge Cambridge University Press 2018 1 Online-Ressource (xiii, 573 Seiten) txt c cr Cambridge studies in advanced mathematics 172 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. Scarabotti, Fabio Tolli, Filippo 1968- Erscheint auch als Druck-Ausgabe 9781107182332 |
| spellingShingle | Ceccherini-Silberstein, Tullio Discrete harmonic analysis representations, number theory, expanders, and the fourier transform |
| title | Discrete harmonic analysis representations, number theory, expanders, and the fourier transform |
| title_auth | Discrete harmonic analysis representations, number theory, expanders, and the fourier transform |
| title_exact_search | Discrete harmonic analysis representations, number theory, expanders, and the fourier transform |
| title_full | Discrete harmonic analysis representations, number theory, expanders, and the fourier transform Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli |
| title_fullStr | Discrete harmonic analysis representations, number theory, expanders, and the fourier transform Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli |
| title_full_unstemmed | Discrete harmonic analysis representations, number theory, expanders, and the fourier transform Tullio Ceccherini-Silberstein, Fabio Scarabotti, Filippo Tolli |
| title_short | Discrete harmonic analysis |
| title_sort | discrete harmonic analysis representations number theory expanders and the fourier transform |
| title_sub | representations, number theory, expanders, and the fourier transform |
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