Uniformity of Strong Asymptotics in Angelesco Systems
Let ₁ and ₂ be two complex-valued Borel measures on the real line such that supp μ₁ = [α₁, ₁] < supp ₂ = [α₂, ₂] and dᵢ()=−ᵢ()d/2πi, where ᵢ() is the restriction to [αᵢ, ᵢ] of a function non-vanishing and holomorphic in some neighborhood of [αᵢ, ᵢ]. Strong asymptotics of multiple orthogonal p...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2025 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/213196 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Uniformity of Strong Asymptotics in Angelesco Systems. Maxim L. Yattselev. SIGMA 21 (2025), 033, 41 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862738476553732096 |
|---|---|
| author | Yattselev, Maxim L. |
| author_facet | Yattselev, Maxim L. |
| citation_txt | Uniformity of Strong Asymptotics in Angelesco Systems. Maxim L. Yattselev. SIGMA 21 (2025), 033, 41 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let ₁ and ₂ be two complex-valued Borel measures on the real line such that supp μ₁ = [α₁, ₁] < supp ₂ = [α₂, ₂] and dᵢ()=−ᵢ()d/2πi, where ᵢ() is the restriction to [αᵢ, ᵢ] of a function non-vanishing and holomorphic in some neighborhood of [αᵢ, ᵢ]. Strong asymptotics of multiple orthogonal polynomials is considered as their multi-indices (₁, 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{₁, ₂}.
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| first_indexed | 2026-03-21T18:41:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213196 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T18:41:33Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Yattselev, Maxim L. 2026-02-16T16:38:26Z 2025 Uniformity of Strong Asymptotics in Angelesco Systems. Maxim L. Yattselev. SIGMA 21 (2025), 033, 41 pages 1815-0659 2020 Mathematics Subject Classification: 42C05; 41A20; 41A25 arXiv:2411.04206 https://nasplib.isofts.kiev.ua/handle/123456789/213196 https://doi.org/10.3842/SIGMA.2025.033 Let ₁ and ₂ be two complex-valued Borel measures on the real line such that supp μ₁ = [α₁, ₁] < supp ₂ = [α₂, ₂] and dᵢ()=−ᵢ()d/2πi, where ᵢ() is the restriction to [αᵢ, ᵢ] of a function non-vanishing and holomorphic in some neighborhood of [αᵢ, ᵢ]. Strong asymptotics of multiple orthogonal polynomials is considered as their multi-indices (₁, 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{₁, ₂}. The research was supported in part by a grant from the Simons Foundation, CGM-706591. The author is grateful to the anonymous referees for their careful reading of the manuscript and helpful suggestions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Uniformity of Strong Asymptotics in Angelesco Systems Article published earlier |
| spellingShingle | Uniformity of Strong Asymptotics in Angelesco Systems Yattselev, Maxim L. |
| title | Uniformity of Strong Asymptotics in Angelesco Systems |
| title_full | Uniformity of Strong Asymptotics in Angelesco Systems |
| title_fullStr | Uniformity of Strong Asymptotics in Angelesco Systems |
| title_full_unstemmed | Uniformity of Strong Asymptotics in Angelesco Systems |
| title_short | Uniformity of Strong Asymptotics in Angelesco Systems |
| title_sort | uniformity of strong asymptotics in angelesco systems |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213196 |
| work_keys_str_mv | AT yattselevmaximl uniformityofstrongasymptoticsinangelescosystems |