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

Olga Holtz; Amos Ron

doi:10.1016/j.jat.2004.10.006

paper

Approximation orders of shift-invariant subspaces of $W_{2}^{s} (R^{d})$

arXiv:math/0512609 · doi:10.1016/j.jat.2004.10.006

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.

49 pages

Cited by in corpus (1)

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Approximation orders of shift-invariant subspaces of W2s​(Rd)

Abstract

Cited by in corpus (1)

Approximation orders of shift-invariant subspaces of $W_{2}^{s} (R^{d})$