Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks
Journal of Approximation Theory
Properties of locally linearly independent refinable function vectors
Journal of Approximation Theory
Vector cascade algorithms and refinable function vectors in Sobolev spaces
Journal of Approximation Theory
Convergence rates of vector cascade algorithms in Lp
Journal of Approximation Theory
Interpolatory quad/triangle subdivision schemes for surface design
Computer Aided Geometric Design
Convergence rates of vector cascade algorithms in Lp
Journal of Approximation Theory
Polynomial-Time Computation of the Joint Spectral Radius for Some Sets of Nonnegative Matrices
SIAM Journal on Matrix Analysis and Applications
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A dilation equation is a functional equation of the form $f(t) = \sum_{k=0}^{N}c_{k}f(2t-k)$, and any nonzero solution of such an equation is called a scaling function. Dilation equations play an important role in several fields, including interpolating subdivision schemes and wavelet theory. This paper obtains sharp bounds for the Holder exponent of continuity of any continuous, compactly supported scaling function in terms of the joint spectral radius of two matrices determined by the coefficients $\{c_{0},\ldots,c_{N}\}$. The arguments lead directly to a characterization of all dilation equations that have continuous, compactly supported solutions.