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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/213196 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Uniformity of Strong Asymptotics in Angelesco Systems. Maxim L. Yattselev. SIGMA 21 (2025), 033, 41 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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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| ISSN: | 1815-0659 |