Fourier analysis on finite groups and applications / Audrey Terras.

Format:

Book

Author/Creator:

Terras, Audrey, author.

Series:

London Mathematical Society student texts ; 43.

London Mathematical Society student texts ; 43

Language:

English

Subjects (All):

Fourier analysis.

Finite groups.

Physical Description:

1 online resource (x, 442 pages) : digital, PDF file(s).

Other Title:

Fourier Analysis on Finite Groups & Applications

Place of Publication:

Cambridge : Cambridge University Press, 1999.

Language Note:

English

Summary:

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.

Contents:

Cover; Title; Copyright; Dedication; Contents; Preface; 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

23 The Trace Formula on Finite Upper Half Planes24 Trace Formula For a Tree and Ihara's Zeta Function; References; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references (p. 421-436) and index.

ISBN:

1-316-08711-5

1-107-36198-2

1-107-36870-7

1-107-36689-5

0-511-62626-6

1-299-40905-9

1-107-36443-4

OCLC:

832441599