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Shift invariant spaces inL2

✍ Scribed by Michael Sand

Publisher
SP Birkhäuser Verlag Basel
Year
1996
Tongue
English
Weight
435 KB
Volume
26
Category
Article
ISSN
0378-620X

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Let s ≥ 1 be an integer, φ s → be a compactly supported function, and S φ denote the linear span of φ • -k k ∈ s . We consider the problem of approximating a continuous function f s → on compact subsets of s from the classes S φ h• , h > 0, based on samples of the function at scattered sites in s .

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The motivation for this work is a recently constructed family of generators of shift invariant spaces with certain optimal approximation properties, but which are not refinable in the classical sense. We try to see whether, once the classical refinability requirement is removed, it is still possible