Video library: P. Thomas, Invertibility threshold for Nevanlinna quotient algebras

VIDEO LIBRARY


Analysis days in Sirius October 28, 2021 11:40, Sochi, online via Zoom at 10:40 CEST (=09:40 BST, =04:40 EDT)

Invertibility threshold for Nevanlinna quotient algebras P. Thomas Institut de Mathématiques de Toulouse
Abstract: Let $\mathcal{N}$ be the Nevanlinna class and let $B$ be a Blaschke product. Consider the natural necessary condition for invertibility of $[f]$ in the quotient algebra $\mathcal{N} / B \mathcal{N}$ : "$\|f\| \ge e^{-H} $ on the zero set of $B$, for some positive harmonic function $H$". For large enough functions $H$, this is almost a sufficient condition if and only if the function $- \log \|B\|$ has a harmonic majorant on the set $\{z\in\mathbb{D}:\rho(z,\Lambda)\geq e^{-H(z)}\}$. We thus study the class of harmonic functions $H$ such that this last condition holds, and give some examples of $B$ where it can be entirely determined. Language: English Website: https://us02web.zoom.us/j/6250951776?pwd=aG5YNkJndWIxaGZoQlBxbWFOWHA3UT09 ^* ID: 625 095 1776, password: pade