Asymptotics of the Lebesgue constants for a $d$-dimensional simplex

Abstract

In this paper an asymptotic formula is given for the Lebesgue constants generated by the anisotropically dilated $d$-dimensional simplex. Contrary to many preceding results established only in dimension two, the obtained ones are proved in any dimension. Also, the "rational" and "irrational" parts are both united and separated in one formula.