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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.04206 |
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Table of Contents:
- Let $μ_1$ and $μ_2$ be two complex-valued Borel measures on the real line such that $\operatorname{supp} μ_1 =[α_1,β_1] < \operatorname{supp} μ_2 =[α_2,β_2]$ and ${\rm d}μ_i(x) = -ρ_i(x){\rm d}x/2π{\rm i}$, where $ρ_i(x)$ is the restriction to $[α_i,β_i]$ of a function non-vanishing and holomorphic in some neighborhood of $[α_i,β_i]$. Strong asymptotics of multiple orthogonal polynomials is considered as their multi-indices $(n_1,n_2)$ tend to infinity in both coordinates. The main goal of this work is to show that the error terms in the asymptotic formulae are uniform with respect to $\min\{n_1,n_2\}$.