Fourier analysis on finite groups and applications

摘要: Introduction Cast of characters Part I: 1. Congruences and the quotient ring integers mod n 1.2 The discrete Fourier transform on finite circle 1.3 Graphs Z/nZ, adjacency operators, eigenvalues 1.4 Four questions about Cayley graphs 1.5 Finite Euclidean three their spectra 1.6 Random walks 1.7 Applications in geometry analysis 1.8 quadratic reciprocity law 1.9 fast 1.10 DFT Abelian groups - tori 1.11 Error-correcting codes 1.12 Poisson sum formula a group 1.13 Some applications chemistry physics 1.14 uncertainty principle II. 2.1 representations 2.2 Induced 2.3 ax + b 2.4 Heisenberg 2.5 symmetric spaces upper half planes Hq 2.6 Special functions K-Bessel spherical 2.7 general linear GL(2, Fq) 2.8. Selberg's trace isospectral non-isomorphic 2.9 2.10 for tree Ihara's zeta function.