Whitney type inequalities for local anisotropic polynomial approximation |
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Authors: | Dinh Dung Tino Ullrich |
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Affiliation: | aVietnam National University, Hanoi, Information Technology Institute, 144, Xuan Thuy, Hanoi, Viet Nam;bHausdorff-Center for Mathematics, 53115 Bonn, Germany |
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Abstract: | We prove a multivariate Whitney type theorem for the local anisotropic polynomial approximation in Lp(Q) with 1≤p≤∞. Here Q is a d-parallelepiped in Rd with sides parallel to the coordinate axes. We consider the error of best approximation of a function f by algebraic polynomials of fixed degree at most ri−1 in variable , and relate it to a so-called total mixed modulus of smoothness appropriate to characterizing the convergence rate of the approximation error. This theorem is derived from a Johnen type theorem on equivalence between a certain K-functional and the total mixed modulus of smoothness which is proved in the present paper. |
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Keywords: | Whitney type inequality Anisotropic approximation by polynomials Total mixed modulus of smoothness Mixed K-functional Sobolev space of mixed smoothness |
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