Audrey Terras
Fourier Analysis on Finite Groups and Applications
Audrey Terras
Fourier Analysis on Finite Groups and Applications
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A friendly introduction to Fourier analysis on finite groups, accessible to undergraduates/graduates in mathematics, engineering and the physical sciences.
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A friendly introduction to Fourier analysis on finite groups, accessible to undergraduates/graduates in mathematics, engineering and the physical sciences.
Produktdetails
- Produktdetails
- Verlag: Cambridge University Press
- Seitenzahl: 456
- Erscheinungstermin: 29. Oktober 2005
- Englisch
- Abmessung: 229mm x 152mm x 27mm
- Gewicht: 735g
- ISBN-13: 9780521457187
- ISBN-10: 0521457181
- Artikelnr.: 21635218
- Verlag: Cambridge University Press
- Seitenzahl: 456
- Erscheinungstermin: 29. Oktober 2005
- Englisch
- Abmessung: 229mm x 152mm x 27mm
- Gewicht: 735g
- ISBN-13: 9780521457187
- ISBN-10: 0521457181
- Artikelnr.: 21635218
Introduction
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.
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.
Introduction
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.
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.