Approximation from locally finite-dimensional shift-invariant spaces

Zhao, Kang

doi:10.1090/S0002-9939-96-03253-4

Approximation from locally finite-dimensional
shift-invariant spaces

Author: Kang Zhao
Journal: Proc. Amer. Math. Soc. 124 (1996), 1857-1867
MSC (1991): Primary 41A15, 41A25, 41A28, 41A63
DOI: https://doi.org/10.1090/S0002-9939-96-03253-4
MathSciNet review: 1307577
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Abstract: After exploring some topological properties of locally finite-dimensional shift-invariant subspaces $S$ of $L_p(\mathbb {R}^s)$ , we show that if $S$ provides approximation order $k$ , then it provides the corresponding simultaneous approximation order. In the case $S$ is generated by a compactly supported function in $L_\infty (\mathbb {R})$ , it is proved that $S$ provides approximation order $k$ in the $L_p(\mathbb {R})$ -norm with $p>1$ if and only if the generator is a derivative of a compactly supported function that satisfies the Strang-Fix conditions.

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