Shift-invariant Spaces on the Real Line
نویسنده
چکیده
We investigate the structure of shift-invariant spaces generated by a finite number of compactly supported functions in Lp(R) (1 ≤ p ≤ ∞). 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 Z. Moreover, we show that such a shiftinvariant space provides Lp-approximation order k if and only if it contains all polynomials of degree less than k.
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