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Alan Sola: Optimal approximants and orthogonal polynomials in several variables

Time: Wed 2020-09-16 13.15 - 14.15

Location: Kräftriket, house 5, room 14

Participating: Alan Sola, Stockholms universitet

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I will report on joint work with M. Sargent (U Arkansas) concerning optimal polynomial approximants and orthogonal polynomials. We will discuss relationships between OAs and orthogonal polynomials in weighted spaces, and explore difficulties that arise in several variables. Weakly inner functions provide extreme cases where nontrivial OPs cannot be recovered from OAs. Concrete examples are presented to illustrate the general theory and are used to disprove certain natural conjectures.