| Description |
1 online resource |
| Series |
London Mathematical Society student texts ; 43 |
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London Mathematical Society student texts ; 43.
|
| Contents |
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 |
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19. Finite Symmetric Spaces -- Finite Upper Half Plane H [subscript q]. 20. Special Functions on H [subscript q] -- K-Bessel and Spherical. 21. The General Linear Group GL(2, F [subscript q]) |
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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 |
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4. Four Questions about Cayley Graphs. 5. Finite Euclidean Graphs and Three Questions about Their Spectra. 6. Random Walks on Cayley Graphs |
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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 |
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pt. 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 |
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pt. 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 |
| Summary |
"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 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."--Jacket |
| Bibliography |
Includes bibliographical references (pages 421-436) and index |
| Notes |
Print version record |
| Subject |
Fourier analysis.
|
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Finite groups.
|
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Fourier Analysis
|
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MATHEMATICS -- Infinity.
|
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Finite groups
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Fourier analysis
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Harmonische Analyse
|
| Form |
Electronic book
|
| ISBN |
9781107361980 |
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1107361982 |
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9780511626265 |
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0511626266 |
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9781107366893 |
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1107366895 |
|
