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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2411.04206 |
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| _version_ | 1866910932154712064 |
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| author | Yattselev, Maxim L. |
| author_facet | Yattselev, Maxim L. |
| 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 $\min\{n_1,n_2\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04206 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniformity of Strong Asymptotics in Angelesco Systems Yattselev, Maxim L. Classical Analysis and ODEs 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 $\min\{n_1,n_2\}$. |
| title | Uniformity of Strong Asymptotics in Angelesco Systems |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.04206 |