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On Equivalence of Moduli of Smoothness

✍ Scribed by Yingkang Hu

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
128 KB
Volume
97
Category
Article
ISSN
0021-9045

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✦ Synopsis

Its inverse with any constants independent of f is not true in general. Hu and Yu proved that the inverse holds true for splines S with equally spaced knots, thus | m (S, t) p t t| m&1 (S$, t) p tt 2 | m&2 (S", t) p } } } . In this paper, we extend their results to splines with any given knot sequence, and further to principal shift-invariant spaces and wavelets under certain conditions. Applications are given at the end of the paper.

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