A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Tullio Ceccherini-Silberstein is Professor of Mathematical Analysis at Università del Sannio, Benevento. He is also an Editor of the EMS journal Groups, Geometry, and Dynamics. He has written over 90 research articles on topics ranging from functional and harmonic analysis to group theory, ergodic theory and dynamical systems, and theoretical computer sciences. He has also co-authored four monographs and four proceedings volumes.
Inhaltsangabe
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).
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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