On convergence of partial derivatives of multivariate Bernstein polynomials

Alexander Veretennikov; Evguenia Veretennikova

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arXiv · 1507.05235

On convergence of partial derivatives of multivariate Bernstein polynomials

Alexander Veretennikov·Evguenia Veretennikova

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Abstract

It is be shown that the sequence of Bernstein polynomials for a function of several variables converges to this function uniformly along with every partial derivative of any order, provided that the latter derivative is well defined and continuous. This may be interesting in some questions of stochastic calculus, in particular, in a methodical proof of multidimensional Ito's formula based on the product rule.

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Alexander Veretennikov, Evguenia Veretennikova. 2015-07-18. On convergence of partial derivatives of multivariate Bernstein polynomials. https://arxiv.org/abs/1507.05235

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