Myrto Manolaki (UCD)

will speak on

Optimal polynomial approximants

Time: 4:00PM
Date: Tue 13th November 2018
Location: Seminar Room SCN 1.25 [map]

Abstract: Given a Hilbert space $H$ of analytic functions on the unit disc and a function $f$ in $H$, a polynomial $p_n$ is called an optimal polynomial approximant of degree $n$ of $1/f$ if $p_n$ minimizes $\|pf - 1\|$ over all polynomials $p$ of degree at most $n$. This notion was introduced to investigate the phenomenon of cyclicity in certain function spaces, including the classical Hardy, Bergman and Dirichlet spaces. In this talk, we will discuss the behaviour of the sequence of optimal polynomial approximants on subsets of the unit circle. Our main theorem uses a new result on simultaneous zero-free approximation, which is of independent interest.

(Joint work with Catherine B\'en\'eteau, Oleg Ivrii and Daniel Seco.)

(This talk is part of the Analysis series.)

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