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Fourier Analysis on Finite Groups and Applications

Fourier Analysis on Finite Groups and Applications

$72.99 (P)

Part of London Mathematical Society Student Texts

  • Date Published: March 1999
  • availability: Available
  • format: Paperback
  • isbn: 9780521457187

$ 72.99 (P)

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About the Authors
  • This book gives a friendly introduction to Fourier analysis on finite groups, both commutative and noncommutative. Aimed at students in mathematics, engineering and the physical sciences, it examines the theory of finite groups in a manner 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. The author divides the book into two parts. In the first part, she parallels the development of Fourier analysis on the real line and the circle, and then moves on to analog of higher dimensional Euclidean space. The second part emphasizes matrix groups such as the Heisenberg group of upper triangular 2x2 matrices with 1's down the diagonal and entries in a finite field. The book concludes with an introduction to zeta functions on finite graphs via the trace formula.

    • An accessible introduction to the topic
    • Area has become popular in recent years, due to the wide range of applications
    • Author is recognised in the field
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    Reviews & endorsements

    "The book certainly contains a wealth of information...a rewarding pleasure to leaf through its pages." Mathematical Reviews

    "...Not merely readable but entertaining and also easy to browse, this book should help lift undergraduate mathematics to a higher level of mathematical sophistication and maturity. Highly recommended." Choice

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    Product details

    • Date Published: March 1999
    • format: Paperback
    • isbn: 9780521457187
    • length: 456 pages
    • dimensions: 229 x 152 x 26 mm
    • weight: 0.67kg
    • contains: 64 b/w illus.
    • availability: Available
  • Table of Contents

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

  • Author

    Audrey Terras, University of California, San Diego

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