Multivariate wavelet frames / by Maria Skopina, Aleksandr Krivoshein, Vladimir Protasov.

Preface; Contents; About the Authors; Basic Notation; 1 Bases and Frames in Hilbert Spaces; 1.1 Riesz Bases; 1.2 Frames ; 2 MRA-Based Wavelet Bases and Frames; 2.1 Dilation Matrix; 2.2 Shift-Invariant Systems and Bracket Product; 2.3 Multiresolution Analysis; 2.4 MRA-Based Wavelets and Matrix Extension Principle; 2.5 Matrix Extension Problem; 2.6 Refinable Functions; 2.7 Conditions of Biorthogonality; References; 3 Construction of Wavelet Frames Generated by MEP; 3.1 Sufficient Frame Conditions; 3.2 Approximation Order and Vanishing Moments; 3.3 Polyphase Characterization of Vanishing Moments

3.4 Construction of Compactly Supported Frames3.5 Examples; References; 4 Frame-Like Wavelet Expansions; 4.1 Dual Frame-Like Systems; 4.2 Scaling Expansions; 4.3 Wavelet Expansions; 4.4 Examples; References; 5 Symmetric Wavelets; 5.1 Symmetric Refinable Masks; 5.2 Interpolatory Symmetric Wavelets; 5.3 Symmetric Frame-Like Wavelets and Dual Wavelet Frames; 5.4 Examples; References; 6 Smoothness of Wavelets; 6.1 Tiles, Self-similar Tilings, and Supports of Refinable Functions; 6.2 The Matrix Method of Computing the Hölder Regularity; 6.3 Special Cases and Examples

6.4 Construction of the Continuous Refinable Function6.5 Proofs of the Main Theorems; 6.6 Derivatives of Refinable Functions; 6.7 Modulus of Continuity of a Refinable Function; 6.8 Refinement Equations in Lp.; 6.9 Computation of the Joint Spectral Radius; References; Bibliography; Index