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...
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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2018
|
| Series: | Cambridge studies in advanced mathematics
172 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBA01 UBR01 UER01 Volltext |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 20 Jun 2018) |
| Physical Description: | 1 Online-Ressource (xiii, 573 Seiten) |
| ISBN: | 9781316856383 |
| DOI: | 10.1017/9781316856383 |
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| 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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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9781316856383 |
| language | English |
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| physical | 1 Online-Ressource (xiii, 573 Seiten) |
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| spelling | Ceccherini-Silberstein, Tullio 1966- Verfasser (DE-588)134288920 aut 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 rdacontent c rdamedia cr rdacarrier Cambridge studies in advanced mathematics 172 Title from publisher's bibliographic system (viewed on 20 Jun 2018) 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 Harmonic analysis Fourier transformations Finite groups Finite fields (Algebra) Scarabotti, Fabio 1966- Verfasser (DE-588)134289013 aut Tolli, Filippo 1968- Verfasser (DE-588)13428903X aut Erscheint auch als Druck-Ausgabe 978-1-107-18233-2 Cambridge studies in advanced mathematics 172 (DE-604)BV044781283 172 https://doi.org/10.1017/9781316856383 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Ceccherini-Silberstein, Tullio 1966- Scarabotti, Fabio 1966- Tolli, Filippo 1968- Discrete harmonic analysis representations, number theory, expanders, and the fourier transform Cambridge studies in advanced mathematics Harmonic analysis Fourier transformations Finite groups Finite fields (Algebra) |
| 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 |
| topic | Harmonic analysis Fourier transformations Finite groups Finite fields (Algebra) |
| topic_facet | Harmonic analysis Fourier transformations Finite groups Finite fields (Algebra) |
| url | https://doi.org/10.1017/9781316856383 |
| volume_link | (DE-604)BV044781283 |
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