Sharp estimates of the solutions to B{\'e}zout's polynomial equation and a corona theorem
Classical Analysis and ODEs
2022-05-03 v1 Complex Variables
Abstract
In this paper, we obtain estimates for the solutions to the classical B{\'e}zout equation that are analogous to Carleson's solution to the corona theorem for the bounded analytic functions on the open unit disk. As an application, we extend some results of Luo and obtain a corona theorem for the multipliers of a class of de Branges--Rovnyak spaces.
Keywords
Cite
@article{arxiv.2205.00740,
title = {Sharp estimates of the solutions to B{\'e}zout's polynomial equation and a corona theorem},
author = {Emmanuel Fricain and Andreas Hartmann and Ross William T. and Dan Timotin},
journal= {arXiv preprint arXiv:2205.00740},
year = {2022}
}