A generalized modulus of smoothness

Draganov, Borislav; Ivanov, Kamen

doi:10.1090/S0002-9939-2014-11884-3

A generalized modulus of smoothness
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by Borislav R. Draganov and Kamen G. Ivanov PDF

Proc. Amer. Math. Soc. 142 (2014), 1577-1590 Request permission

Abstract:

We construct moduli of smoothness that generalize the well-known classical moduli and possess similar properties. They are related to a linear differential operator $L$ just as the classical moduli are related to the ordinary derivative. The generalized moduli are used to characterize the approximation error of the corresponding $L$-splines in $L_p [a,b]$, $1\le p\le \infty$.

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