Error bounds of potential theoretic numerical integration formulas in weighted Hardy spaces

Abstract

We give a mathematical analysis of potential-theoretical numerical integration formulas mainly proposed by Tanaka et al. over weighted Hardy spaces, which are spaces of analytic functions with a certain decay. We investigate the case of choosing sampling points by discrete energy minimization. In order to bound the convergence rate of the numerical integration error, we make use of the recent result of Hayakawa and Tanaka on the function approximation formula.