Fourier analysis on finite abelian groups
Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, cryptography, algorithms, and sequence design. This self-contained book provides a thorough look at the Fourier transform, one of the most useful tools in applied...
Enregistré dans:
| Hovedforfatter: | |
|---|---|
| Format: | Livre numérique |
| Sprog: | Anglais |
| Udgivet: |
Boston, MA :
Birkhäuser Boston
[20..].
Cham : Springer Nature |
| Udgivelse: | 1st ed. 2009. |
| Serier: | Applied and Numerical Harmonic Analysis
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| Online adgang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Kommentar: |
Description d'après consultation du 06 mars 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Fourier Analysis on Finite Abelian Groups, Texte imprimé, 9780817649173 • Fourier analysis on finite Abelian groups, Bao Luong, Boston, Birkhäuser, 2009, 1 vol. (xvi-156 p.), Applied and numerical harmonic analysis, 0-8176-4915-8 |
Indholdsfortegnelse:
- Preface Overview Chapter 1: Foundation Material Results from Group Theory Quadratic Congruences Chebyshev Systems of Functions Chapter 2: The Fourier Transform A Special Class of Linear Operators Characters The Orthogonal Relations for Characters The Fourier Transform The Fourier Transform of Periodic Functions The Inverse Fourier Transform The Inversion Formula Matrices of the Fourier Transform Iterated Fourier Transform Is the Fourier Transform a Self-Adjoint Operator? The Convolutions Operator Banach Algebra The Uncertainty Principle The Tensor Decomposition The Tensor Decomposition of Vector Spaces The Fourier Transform and Isometries Reduction to Finite Cyclic Groups Symmetric and Antisymmetric Functions Eigenvalues and Eigenvectors Spectrak Theorem Ergodic Theorem Multiplicities of Eigenvalues The Quantum Fourier Transform Chapter 3: Quadratic Sums 1. The Number G_n(1) Reduction Formulas.