Proceedings of the American Mathematical Society

Author(s): Rong-Qing Jia
Journal: Proc. Amer. Math. Soc. 125 (1997), 785-793.
MSC (1991): Primary 41A25, 41A15, 46E30
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Abstract: We investigate the structure of shift-invariant spaces generated by a finite number of compactly supported functions in $L_p(\mathbb R )$ $(1\le p\le \infty )$ . Based on a study of linear independence of the shifts of the generators, we characterize such shift-invariant spaces in terms of the semi-convolutions of the generators with sequences on $\mathbb Z$ . Moreover, we show that such a shift-invariant space provides $L_p$

-approximation order $k$

if and only if it contains all polynomials of degree less than $k$

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