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Discrete harmonic analysis: representations, number theory, expanders, and the Fourier transform

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Author(s): Ceccherini-Silberstein, Tullio; Scarabotti, Fabio; Tolli, Filippo
Series: Cambridge studies in advanced mathematics 172
Publisher: Cambridge University Press
Year: 2018

Language: English
Pages: 573
City: Cambridge

Content: 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).