Strong asymptotics for the Pollaczek multiple orthogonal polynomials ensembles

2014/10/06 by A. I. Aptekarev, Aptekarev, A. I., G. Lopez Lagomasino +3
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1410.1261

38 pages, 7 figures

arxiv created 2014/10/06 · arxiv updated 2014/10/07

Abstract

We study the asymptotic properties of a class of multiple orthogonal polynomials with respect to a Nikishin system generated by two measures (σ₁, σ₂) with unbounded supports (supp(σ₁) ⊂ ℝ₊, supp(σ₂) ⊂ ℝ_-), and such that the second measure σ₂ is discrete. The weak asymptotics for these polynomials was obtained previously by V. Sorokin. We use his result and the Riemann-Hilbert analysis to derive the strong asymptotics of these polynomials and of the reproducing kernel.

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