Lower Bound for the Lebesgue Function of an Interpolation Process with Algebraic Polynomials on Equidistant Nodes of a Simplex

摘要

For an interpolation process with algebraic polynomials of degree n on equidistant nodes of an m-simplex for m ≥ 2, we obtain a pointwise lower bound for the Lebesgue function similar to the well-known estimate for interpolation on a closed interval.