Multidimensional pseudo-Leja sequences

2023/03/21 by Dimitri Jordan Kenne, Kenne, Dimitri Jordan
Mathematics · #32E30 #41A05 #41A63 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2303.11871

openalex publication_date 2023/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The one-dimensional pseudo Leja sequences introduced in \citebialas2012pseudo, 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 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.

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