Speaker: Abey Lopez-Garcia (UCF, Mathematics Dept.)
Title: Relative asymptotics of multiorthogonal polynomials for Nikishin systems of two measures
Abstract: In this talk I will discuss the relative asymptotics of two sequences of multiorthogonal polynomials associated to two Nikishin systems of measures on the real line, the second one of which is obtained from the first one perturbing the generating measures with non-negative integrable functions. Each Nikishin system consists of two measures. The study of relative asymptotics in the scalar case was initiated in the 1970s and 1980s by Gonchar, Rakhmanov, and Máté- Nevai-Totik, and it is one of the standard forms of asymptotics studied for orthogonal polynomials (other forms are strong, ratio, and nth root asymptotics). The result discussed is obtained in the context of Nikishin systems of two measures. The technique employed for the analysis is based on an adaptation of a fixed-point theorem technique developed by A. Aptekarev for the study of strong asymptotics of multiorthogonal polynomials for Nikishin systems. This is a joint work with G. Lopez Lagomasino.
Place: https://ucf.zoom.us/j/96789802247
Meeting ID: 967 8980 2247
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