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Approximation orders of shift-invariant subspaces of $W^s_2({\Bbb R}^d)$

Olga Holtz·Amos Ron
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Abstract

We extend the existing theory of approximation orders provided by shift-invariant subspaces of $L_2$ to the setting of Sobolev spaces, provide treatment of $L_2$ cases that have not been covered before, and apply our results to determine approximation order of solutions to a refinement equation with a higher-dimensional solution space.

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Olga Holtz, Amos Ron. 2005-12-27. Approximation orders of shift-invariant subspaces of $W^s_2({\Bbb R}^d)$. https://doi.org/10.1016/j.jat.2004.10.006

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