Multidimensional pseudo-Leja sequences

Abstract

The one-dimensional pseudo Leja sequences introduced in \cite{bialas2012pseudo}, as an alternative to Leja sequences, provides us with good interpolation nodes for the approximation of holomorphic functions. We propose a definition of multidimensional pseudo Leja sequences associated to a compact set $K$ of the complex space $\mathbb{C}^p$ which generalises both the one-dimensional version and the multidimensional Leja sequences. We show that these sequences can be used to calculate the transfinite diameter of $K$. We also present a relation to the pluricomplex Green function associated to $K$. Subsequently, we show that the intertwinning of pseudo Leja sequences is still a pseudo Leja sequence. We give a method to compute pseudo Leja sequences with the help of discrete meshes.