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}
}
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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