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RIEMANN-HILBERT HIERARCHIES FOR HARD EDGE PLANAR ORTHOGONAL POLYNOMIALS
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). ; Department Of Mathematics And Computer Sciences, ST. Petersburg State University, St. Petersburg, Russia; Department Of Mathematics And Statistics, University Of Reading, Reading, UK.ORCID iD: 0000-0002-4971-7147
School Of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel; Department Of Mathematics, Ku Leuven, B-3001, Leuven, Belgium.
2024 (English)In: American Journal of Mathematics, ISSN 0002-9327, E-ISSN 1080-6377, Vol. 146, no 2, p. 371-403Article in journal (Refereed) Published
Abstract [en]

We obtain a full asymptotic expansion for orthogonal polynomials with respect to weighted area measure on a Jordan domain D with real-analytic boundary. The weight is fixed and assumed to be real-analytically smooth and strictly positive, and for any given precision κ, the expansion holds with an O(N−κ−1) error in N-dependent neighborhoods of the exterior region as the degree N tends to infinity. The main ingredient is the derivation and analysis of Riemann-Hilbert hierarchies—sequences of scalar Riemann-Hilbert problems—which allows us to express all higher order correction terms in closed form. Indeed, the expansion may be understood as a Neumann series involving an explicit operator. The expansion theorem leads to a semiclassical asymptotic expansion of the corresponding hard edge probability wave function in terms of distributions supported on ∂D.

Place, publisher, year, edition, pages
Johns Hopkins University Press , 2024. Vol. 146, no 2, p. 371-403
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-345234DOI: 10.1353/ajm.2024.a923237Scopus ID: 2-s2.0-85189073398OAI: oai:DiVA.org:kth-345234DiVA, id: diva2:1850514
Note

QC 20240411

Available from: 2024-04-10 Created: 2024-04-10 Last updated: 2024-04-11Bibliographically approved

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Hedenmalm, Håkan

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