Strong asymptotics for the Pollaczek multiple orthogonal polynomials ensembles

doi:https://doi.org/10.48550/arxiv.1410.1261

Open AccessPreprint10.48550/arxiv.1410.1261

Strong asymptotics for the Pollaczek multiple orthogonal polynomials ensembles

Alexander Ivanovich Aptekarev,G. López Lagomasino,Martinez-Finkelshtein, A.-2014-10-06-arXiv (Cornell University)

TL;DRAbstract

We study the asymptotic properties of a class of multiple orthogonal polynomials with respect to a Nikishin system generated by two measures $(σ_1, σ_2)$ with unbounded supports (${supp}(σ_1) \subset \mathbb{R}_+$, ${supp}(σ_2) \subset \mathbb{R}_-$), and such that the second measure $σ_2$ 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.

Chat with Paper

AI Agents for this Paper

We study the asymptotic properties of a class of multiple orthogonal polynomials with respect to a Nikishin system generated by two measures $(σ_1, σ_2)$ with unbounded supports (${supp}(σ_1) \subset \mathbb{R}_+$, ${supp}(σ_2) \subset \mathbb{R}_-$), and such that the second measure $σ_2$ 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.

Keywords

Orthogonal polynomialsMathematicsClassical orthogonal polynomialsApplied mathematicsStatistical physicsPure mathematicsMathematical analysisAlgebra over a field

Chat

Click to start Chat