Fourier Analysis on Finite Abelian Groups

• Κύριος συγγραφέας: Luong, Bao (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Boston : Birkhäuser Boston, 2009.
• Σειρά: Applied and Numerical Harmonic Analysis
• Θέματα: Mathematics.; Algebra.; Group theory.; Mathematical analysis.; Analysis (Mathematics).; Fourier analysis.; Analysis.; Fourier Analysis.; Group Theory and Generalizations.

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...

Πίνακας περιεχομένων:

• 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.