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Discrete Fourier Analysis

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Cover of 'Discrete Fourier Analysis'

Table of Contents

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    Book Overview
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    Chapter 1 The Finite Fourier Transform
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    Chapter 2 Translation-Invariant Linear Operators
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    Chapter 3 Circulant Matrices
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    Chapter 4 Convolution Operators
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    Chapter 5 Fourier Multipliers
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    Chapter 6 Eigenvalues and Eigenfunctions
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    Chapter 7 The Fast Fourier Transform
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    Chapter 8 Time-Frequency Analysis
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    Chapter 9 Time-Frequency Localized Bases
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    Chapter 10 Wavelet Transforms and Filter Banks
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    Chapter 11 Haar Wavelets
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    Chapter 12 Daubechies Wavelets
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    Chapter 13 The Trace
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    Chapter 14 Hilbert Spaces
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    Chapter 15 Bounded Linear Operators
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    Chapter 16 Self-Adjoint Operators
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    Chapter 17 Compact Operators
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    Chapter 18 The Spectral Theorem
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    Chapter 19 Schatten–von Neumann Classes
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    Chapter 20 Fourier Series
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    Chapter 21 Fourier Multipliers on $$\mathbb{S}^{1}$$
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    Chapter 22 Pseudo-Differential Operators on $$\mathbb{S}^{1}$$
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    Chapter 23 Pseudo-Differential Operators on $$\mathbb{Z}$$
Attention for Chapter 6: Eigenvalues and Eigenfunctions
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