Approximation orders of shift-invariant subspaces of \(W_{2}^{s}(\mathbb R^d)\) (Q1763782)
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| Language | Label | Description | Also known as |
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| English | Approximation orders of shift-invariant subspaces of \(W_{2}^{s}(\mathbb R^d)\) |
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Approximation orders of shift-invariant subspaces of \(W_{2}^{s}(\mathbb R^d)\) (English)
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22 February 2005
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The authors discuss approximation orders of shift-invariant spaces in Sobolev spaces. First, they characterize in Theorem 21 the approximation orders provided by finitely generated shift-invariant (FSI) spaces by means of the Fourier transforms of the generators, extending a result of de \textit{C. Boor, R. A. de Vore} and \textit{A. Ron} [Trans. Am. Math. Soc. 341, No. 2, 787--806 (1994; Zbl 0790.41012)] from the \(L^2\) space to Sobolev spaces. Then they prove the existence of a superfunction and discuss its behavior (good or bad superfunction). Finally, approximation orders, Strang-Fix type conditions, and polynomial reproductions are investigated for FSI generators associated with matrix refinement equations.
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approximation order
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shift-invariant space
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refinement equation
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superfunction
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