Logarithmic asymptotic of multi-level Hermite-Padé polynomials

Abstract

We study the logarihtnmic asymptotic of multiple orthogonal polynomials arising in a mixed type Hermite-Padé approximation problem associated with the rational perturbation of a Nikishin system of functions. The formulas obtained allow to give exact estimates of the rate of convergence of the corresponding Hermite-Padé approximants.

17 pages. arXiv admin note: text overlap with arXiv:1904.00126