# Solutions in Sobolev spaces of vector refinement equations with a general dilation matrix

@article{Han2006SolutionsIS, title={Solutions in Sobolev spaces of vector refinement equations with a general dilation matrix}, author={Bin Han}, journal={Adv. Comput. Math.}, year={2006}, volume={24}, pages={375-403} }

- Published 2006 in Adv. Comput. Math.
DOI:10.1007/s10444-004-7615-2

In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space W k p (R)(1 6 p 6 ∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented. Rate of convergence of vector cascade algorithms in a Sobolev space W k p (R) will be investigated. When the dilation matrix is isotropic, a characterization will be given for the Lp(1 6 p 6 ∞) critical smoothness exponent of a refinable function… CONTINUE READING

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