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Frames of Periodic Shift-Invariant Spaces

โœ Scribed by Di-Rong Chen


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
105 KB
Volume
107
Category
Article
ISSN
0021-9045

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๐Ÿ“œ SIMILAR VOLUMES


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Let s โ‰ฅ 1 be an integer, ฯ† s โ†’ be a compactly supported function, and S ฯ† denote the linear span of ฯ† โ€ข -k k โˆˆ s . We consider the problem of approximating a continuous function f s โ†’ on compact subsets of s from the classes S ฯ† hโ€ข , h > 0, based on samples of the function at scattered sites in s .

Wavelet Decompositions of Nonrefinable 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

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Under certain assumptions on the compactly supported function f ยฅ C(R d ), we propose two methods of selecting a function s from the scaled principal shiftinvariant space S h (f) such that s interpolates a given function f at a scattered set of data locations. For both methods, the selection scheme

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We construct right shift invariant subspaces of index n, 1 [ n [ ., in a p spaces, 2 < p < ., and in weighted a p spaces.

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In this paper the rearrangement-invariant hulls and kernels of the classes loc ] on a noncompact nondiscrete locally compact abelian group are characterized. The space L 1 loc & S$ of tempered distributions serves as the extended domain of the Fourier transform instead of the classical domain L 1 +