New polynomial preserving operators on simplices: direct results
نویسندگان
چکیده
A new class of differential operators on the simplex is introduced, which define weighted Sobolev norms andwhose eigenfunctions are orthogonal polynomialswith respect to Jacobiweights. These operators appear naturally in the study of quasi-interpolants which are intermediate between Bernstein– Durrmeyer operators and orthogonal projections on polynomial subspaces. The quasi-interpolants satisfy a Voronovskaja-type identity and a Jackson–Favard-type error estimate. These and further properties follow from a spectral analysis of the differential operators. The results are based on a pointwise orthogonality relation of Bernstein polynomials that was recently discovered by the authors. © 2004 Elsevier Inc. All rights reserved.
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ورودعنوان ژورنال:
- Journal of Approximation Theory
دوره 131 شماره
صفحات -
تاریخ انتشار 2004