Strong Asymptotics of Hermite-Pad\'e Approximants for Angelesco Systems
Maxim L. Yattselev
TL;DR
This paper derives strong asymptotic formulas for type II Hermite-Padé approximants applied to Angelesco systems with complex weights, expanding understanding of their behavior for disjoint interval supports.
Contribution
It provides the first comprehensive derivation of strong asymptotics for Hermite-Padé approximants in Angelesco systems with complex weights.
Findings
Strong asymptotics formulas are established for any ray sequence of multi-indices.
Results apply to vector Cauchy transforms of Jacobi-type densities supported on disjoint intervals.
The work advances the theoretical understanding of Hermite-Padé approximants in complex-weight Angelesco systems.
Abstract
In this work type II Hermite-Pad\'e approximants for a vector of Cauchy transforms of smooth Jacobi-type densities are considered. It is assumed that densities are supported on mutually disjoint intervals (an Angelesco system with complex weights). The formulae of strong asymptotics are derived for any ray sequence of multi-indices.
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