Whitney's theorem for local anisotropic polynomial L_p-approximation, 0

2013/06/10 by Dũng, Dinh, Van Dũng, Nguyen, Hoa, Nguyen Dinh
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1306.2093

Abstract

Dinh Dũng and T. Ullrich have proven a multivariate Whitney's theorem for the local anisotropic polynomial approximation in L_p(Q) for 1 ≤ p ≤ ∞, where Q is a d-parallelepiped in \RR^d with sides parallel to the coordinate axes. They considered the error of best approximation of a function f by algebraic polynomials of fixed degree at most r_i - 1 in variable x_i, i=1,...,d. The convergence rate of the approximation error when the size of Q going to 0 is characterized by a so-called total mixed modulus of smoothness. The method of proof used by these authors is not suitable to the case 0

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