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Quasi-Interpolation in Shift Invariant Spaces

โœ Scribed by H.N. Mhaskar; F.J. Narcowich; J.D. Ward

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
83 KB
Volume
251
Category
Article
ISSN
0022-247X

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โœฆ Synopsis

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 . We demonstrate how classical polynomial inequalities lead to the construction of local, quasi-interpolatory operators for this purpose.

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