Geometry Seminar - Abstracts


Tuesday 7 June 2022, 16:00 - 17:00 in HG03.085
Pablo Román (UN Córdoba)
Riemann-Hilbert problems for matrix orthogonal polynomials, asymptotics and weight decompositions


In this talk, we consider the Riemman-Hilbert characterization for matrix valued orthogonal polynomials. By applying the steepest descent method to the Riemann-Hilbert problem, we obtain the asymptotic behavior of the polynomials as the degree tends to infinity. We give a detailed analysis for families of matrix valued Jacobi and Gegenbauer polynomials that arise from the harmonic analysis of compact symmetric spaces. In these cases, the representation theory gives a natural decomposition of the weight matrix that plays a role in the asymptotic analysis.

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