Ten lectures on wavelets
Two-scale difference equations II. local regularity, infinite products of matrices and fractals
SIAM Journal on Mathematical Analysis
Characterizations of Scaling Functions: Continuous Solutions
SIAM Journal on Matrix Analysis and Applications
Wavelet analysis of refinement equations
SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Convergence of cascade algorithms
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Multivariate refinement equations and convergence of subdivision schemes
SIAM Journal on Mathematical Analysis
Accuracy of lattice translates of several multidimensional refinable functions
Journal of Approximation Theory
Vector subdivision schemes and multiple wavelets
Mathematics of Computation
Smoothness of Multiple Refinable Functions and Multiple Wavelets
SIAM Journal on Matrix Analysis and Applications
Analysis and construction of optimal multivariate biorthogonal wavelets with compact support
SIAM Journal on Mathematical Analysis
Multiple refinable Hermite interpolants
Journal of Approximation Theory
The Sobolev regularity of refinable functions
Journal of Approximation Theory
Approximation properties and construction of Hermite interpolants and biorthogonal mutliwavelets
Journal of Approximation Theory
Computing the Smoothness Exponent of a Symmetric Multivariate Refinable Function
SIAM Journal on Matrix Analysis and Applications
Spectral Analysis of the Transition Operator and Its Applications to Smoothness Analysis of Wavelets
SIAM Journal on Matrix Analysis and Applications
Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks
Journal of Approximation Theory
Honeycomb and k-fold Hermite subdivision schemes
Journal of Computational and Applied Mathematics
Approximation with scaled shift-invariant spaces by means of quasi-projection operators
Journal of Approximation Theory
Dyadic C2 Hermite interpolation on a square mesh
Computer Aided Geometric Design
Vector refinement equations with infinitely supported masks
Journal of Approximation Theory
Subdivisions with infinitely supported mask
Journal of Computational and Applied Mathematics
Generalized interpolating refinable function vectors
Journal of Computational and Applied Mathematics
Dyadic C2 Hermite interpolation on a square mesh
Computer Aided Geometric Design
Honeycomb and k-fold Hermite subdivision schemes
Journal of Computational and Applied Mathematics
Scalar multivariate subdivision schemes and box splines
Computer Aided Geometric Design
Symmetric orthogonal filters and wavelets with linear-phase moments
Journal of Computational and Applied Mathematics
A generalized Taylor factorization for Hermite subdivision schemes
Journal of Computational and Applied Mathematics
From Hermite to stationary subdivision schemes in one and several variables
Advances in Computational Mathematics
Decompositions of trigonometric polynomials with applications to multivariate subdivision schemes
Advances in Computational Mathematics
Bessel multiwavelet sequences and dual multiframelets in Sobolev spaces
Advances in Computational Mathematics
Journal of Approximation Theory
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In this paper we shall study vector cascade algorithms and refinable function vectors with a general isotropic dilation matrix in Sobolev spaces. By introducing the concept of a canonical mask for a given matrix mask and by investigating several properties of the initial function vectors in a vector cascade algorithm, we are able to take a relatively unified approach to study several questions such as convergence, rate of convergence and error estimate for a perturbed mask of a vector cascade algorithm in a Sobolev space Wpk(Rs) (1 ≤ p ≤ ∞, k ∈ N ∪ {0}). We shall characterize the convergence of a vector cascade algorithm in a Sobolev space in various ways. As a consequence, a simple characterization for refinable Hermite interpolants and a sharp error estimate of a vector cascade algorithm in a Sobolev space with a perturbed mask will be presented. The approach in this paper enables us to answer some unsolved questions in the literature on vector cascade algorithms and to comprehensively generalize and improve results on scalar cascade algorithms and scalar refinable functions to the vector case.