On Equivalence of Moduli of Smoothness |
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| Authors: | Yingkang Hu |
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| Institution: | Department of Mathematics and Computer Science, Georgia Southern University, Statesboro, Georgia, 30460-8093, U.S.A. |
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| Abstract: | It is known that iff Wkp, thenωm(f, t)p tωm−1(f′, t)p…. Its inverse with any constants independent offis not true in general. Hu and Yu proved that the inverse holds true for splinesSwith equally spaced knots, thusωm(S, t)p tωm−1(S′, t)pt2ωm−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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| Keywords: | modulus of smoothness splines shift-invariant spaces wavelets degree of approximation convex approximation |
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