Methods of Applied Fourier Analysis
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Boston, MA
Birkhäuser
1998, 1998
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| Edition: | 1st ed. 1998 |
| Series: | Applied and Numerical Harmonic Analysis
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 4.6 Proof of the Commutant Lifting Theorem
- 4.7 Problems
- 5 Harmonic Analysis in Euclidean Space
- 5.1 Function Spaces on Rn
- 5.2 The Fourier Transform on L1
- 5.3 Convolution and Approximation
- 5.4 The Fourier Transform: L2 Theory
- 5.5 Fourier Transform of Measures
- 5.6 Bochner’s Theorem
- 5.7 Problems
- 6 Distributions
- 6.1 General Distributions
- 6.2 Two Theorems on Distributions
- 6.3 Schwartz Space
- 6.4 Tempered Distributions
- 6.5 Sobolev Spaces
- 6.6 Problems
- 7 Functions with Restricted Transforms
- 7.1 General Definitions and the Sampling Formula
- 7.2 The Paley-Wiener Theorem
- 7.3 Sampling Band-Limited Functions
- 7.4 Band-Limited Functions and Information
- 7.5 Problems
- 8 Phase Space
- 8.1 The Uncertainty Principle
- 8.2 The Ambiguity Function
- 8.3 Phase Space and Orthonormal Bases
- 8.4 The Zak Transform and the Wilson Basis
- 8.5 AnApproximation Theorem
- 8.6 Problems
- 9 Wavelet Analysis
- 9.1 Multiresolution Approximations
- 9.2 Wavelet Bases
- 9.3 Examples
- 9.4 Compactly Supported Wavelets
- 9.5 Compactly Supported Wavelets II
- 9.6 Problems
- A The Discrete Fourier Transform
- B The Hermite Functions
- 1 Periodic Functions
- 1.1 The Characters
- 1.2 Some Tools of the Trade
- 1.3 Fourier Series: Lp Theory
- 1.4 Fourier Series: L2 Theory
- 1.5 Fourier Analysis of Measures
- 1.6 Smoothness and Decay of Fourier Series
- 1.7 Translation Invariant Operators
- 1.8 Problems
- 2 Hardy Spaces
- 2.1 Hardy Spaces and Invariant Subspaces
- 2.2 Boundary Values of Harmonic Functions
- 2.3 Hardy Spaces and Analytic Functions
- 2.4 The Structure of Inner Functions
- 2.5 The H1 Case
- 2.6 The Szegö-Kolmogorov Theorem
- 2.7 Problems
- 3 Prediction Theory
- 3.1 Introduction to Stationary Random Processes
- 3.2 Examples of Stationary Processes
- 3.3 The Reproducing Kernel
- 3.4 Spectral Estimation and Prediction
- 3.5 Problems
- 4 Discrete Systems and Control Theory
- 4.1 Introduction to System Theory
- 4.2 Translation Invariant Operators
- 4.3 H?Control Theory
- 4.4 The Nehari Problem
- 4.5 Commutant Lifting and Interpolation