An Introduction to Frames and Riesz Bases

Table of Contents

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   Book Overview
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   Chapter 1 Frames in Finite-Dimensional Inner Product Spaces
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   Chapter 2 Infinite-Dimensional Vector Spaces and Sequences
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   Chapter 3 Bases
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   Chapter 4 Bases and Their Limitations
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   Chapter 5 Frames in Hilbert Spaces
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   Chapter 6 Tight Frames and Dual Frame Pairs
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   Chapter 7 Frames Versus Riesz Bases
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   Chapter 8 Selected Topics in Frame Theory
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    Chapter 9 Frames of Translates
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    Chapter 10 Shift-Invariant Systems in $$L^{2}(\mathbb{R})$$
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    Chapter 11 Gabor Frames in $$L^{2}(\mathbb{R})$$
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    Chapter 12 Gabor Frames and Duality
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    Chapter 13 Selected Topics on Gabor Frames
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    Chapter 14 Gabor Frames in $$\ell^{2}(\mathbb{Z}),L^{2}(0,L), \mathbb{C}^{L}$$
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    Chapter 15 General Wavelet Frames in L 2 ( ℝ ) $$ L^{2}(\mathbb{R}) $$
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    Chapter 16 Dyadic Wavelet Frames for L 2 ( ℝ ) $$L^{2}(\mathbb{R})$$
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    Chapter 17 Frame Multiresolution Analysis
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    Chapter 18 Wavelet Frames via Extension Principles
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    Chapter 19 Selected Topics on Wavelet Frames
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    Chapter 20 Generalized Shift-Invariant Systems in $$L^{2}(\mathbb{R}^{d})$$
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    Chapter 21 Frames on Locally Compact Abelian Groups
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    Chapter 22 Perturbation of Frames
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    Chapter 23 Approximation of the Inverse Frame Operator
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    Chapter 24 Expansions in Banach Spaces