TY  - BOOK
AU  - Audrey Terras 
TI  - Fourier analysis on finite groups and applications
T2  - London Mathematical Society Student Texts 
SN  - 9780521457187
AV  - QA403.5 
PY  - 1999///]
CY  - Cambridge, U.K.
PB  - Cambridge University Press
KW  - Mathematics
N1  - Part I - Finite Abelian Groups 
1 - Congruences and the Quotient Ring of the Integers mod n
2 - The Discrete Fourier Transform on the Finite Circle ℤ/nℤ 
3 - Graphs of ℤ/nℤ, Adjacency Operators, Eigenvalues 
4 - Four Questions about Cayley Graphs 
5 - Finite Euclidean Graphs and Three Questions about Their Spectra 
6 - Random Walks on Cayley Graphs 
7 - Applications in Geometry and Analysis. Connections between Continuous and Finite Problems. Dido's Problem for Polygons 
8 - The Quadratic Reciprocity Law 
9 - The Fast Fourier Transform or FFT 
10 - The DFT on Finite Abelian Groups – Finite Tori 
11 - Error-Correcting Codes 
12 - The Poisson Sum Formula on a Finite Abelian Group 
13 - Some Applications in Chemistry and Physics 
14 - The Uncertainty Principle 

Part II - Finite Nonabelian Groups 
15 - Fourier Transform and Representations of Finite Groups 
16 - Induced Representations 
17 - The Finite ax + b Group 
18 - The Heisenberg Group 
19 - Finite Symmetric Spaces–Finite Upper Half Plane Hq
20 - Special Functions on Hq – K-Bessel and Spherical 
21 - The General Linear Group (Expression not displayed)
22 - Selberg's Trace Formula and Isospectral Non-isomorphic Graphs 
23 - The Trace Formula on Finite Upper Half Planes 
24 - Trace Formula For a Tree and Ihara's Zeta Function
N2  - This book gives a friendly introduction to Fourier analysis on finite groups, both commutative and non-commutative. Aimed at students in mathematics, engineering and the physical sciences, it examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research. With applications in chemistry, error-correcting codes, data analysis, graph theory, number theory and probability, the book presents a concrete approach to abstract group theory through applied examples, pictures and computer experiments. In the first part, the author parallels the development of Fourier analysis on the real line and the circle, and then moves on to analogues of higher dimensional Euclidean space. The second part emphasizes matrix groups such as the Heisenberg group of upper triangular 2x2 matrices. The book concludes with an introduction to zeta functions on finite graphs via the trace formula. --- summary provided by publisher
ER  -