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Weighted Moduli of Smoothness and Spline Spaces

✍ Scribed by Anna Kamont

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 215 KB
Volume: 98
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1998.3277

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✦ Synopsis

In this paper we study relations between moduli of smoothness with the step-weight function . and the best approximation by splines with knots uniformly distributed according to the measure with density 1Â.(x). The direct and converse results are obtained for a class of step-weight functions, containing .(x)= -x(1&x); it is well known that the modulus of smoothness corresponding to this . is related to the best polynomial approximation. As a consequence, we obtain relations between the best polynomial and spline approximations.

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