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Discrete Harmonic Analysis Vital Source e-bog
Tullio Ceccherini-Silberstein
(2018)
Cambridge University Press
1.148,00 kr.
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Discrete Harmonic Analysis
Representations, Number Theory, Expanders, and the Fourier Transform
Tullio Ceccherini-Silberstein, Fabio Scarabotti og Filippo Tolli
(2018)
Sprog: Engelsk
Cambridge University Press
1.169,00 kr.
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Detaljer om varen
- Vital Source searchable e-book (Fixed pages)
- Udgiver: Cambridge University Press (Juni 2018)
- ISBN: 9781316865408
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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Bookshelf online: 5 år fra købsdato.
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Print: -1 sider kan printes ad gangen
Copy: højest -1 sider i alt kan kopieres (copy/paste)
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.
Udgiveren oplyser at følgende begrænsninger er gældende for dette produkt:
Print: -1 sider kan printes ad gangen
Copy: højest -1 sider i alt kan kopieres (copy/paste)
Detaljer om varen
- Hardback: 586 sider
- Udgiver: Cambridge University Press (Juni 2018)
- Forfattere: Tullio Ceccherini-Silberstein, Fabio Scarabotti og Filippo Tolli
- ISBN: 9781107182332
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.
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).
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