Discrete Harmonic Analysis: Representations, Number Theory, Expanders, and the Fourier Transform

ISBN-13: 9781107182332 / Angielski / Twarda / 2018 / 586 str.

Tullio Ceccherini-Silberstein; Fabio Scarabotti; Filippo Tolli

Opis

A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.

Recenzje

'... a very good introduction, for researchers-in-training, to the study of discrete harmonic analysis, its various techniques, and its relationship to other branches of mathematics.' Mark Hunacek, The Mathematical Gazette

Spis treści

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).