Discrete Harmonic Analysis

Discrete Harmonic Analysis

Representations, Number Theory, Expanders, and the Fourier Transform

Tolli, Filippo; Ceccherini-Silberstein, Tullio; Scarabotti, Fabio

Cambridge University Press

06/2018

586

Dura

Inglês

9781107182332

15 a 20 dias

960

Descrição não disponível.
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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