On the Lebesgue constant of Leja sequences for the unit disk and its applications to multivariate interpolation

Abstract

We estimate the growth of the Lebesgue constant of any Leja sequence for the unit disk. The main application is the construction of new multivariate interpolation points in a polydisk (and in the Cartesian product of many plane compact sets) whose Lebesgue constant grows (at most) like a polynomial.