Sharp estimates of the solutions to Bézout's polynomial equation and a corona theorem

Emmanuel Fricain (1) , Andreas Hartmann (2) , Dan Timotin (3) , William T. Ross (4)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 IMB - Institut de Mathématiques de Bordeaux
3 IMAR - "Simion Stoilow" Institute of Mathematics
4 Department of Mathematics and Statistics

In this paper, we obtain estimates for the solutions to the classical Bézout 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.

Mots clés: Bézout's equation; de Branges--Rovnyak spaces; corona theorem

Domaines: Variables complexes [math.CV]; Analyse classique [math.CA]

Emmanuel Fricain, Andreas Hartmann, Dan Timotin, William T. Ross. Sharp estimates of the solutions to Bézout's polynomial equation and a corona theorem. The Journal of Geometric Analysis, 2023, 33 (8). ⟨hal-03655845⟩