Séminaire OrléansThe Corona Problem
Tuesday 26 May 2009 14:00 - Orléans - Salle de Séminaire
Carleson`s Corona Theorem from the 1960`s has served as a major motivation for many results in complex function theory, operator theory and harmonic analysis. In its simplest form, the result states that for two bounded analytic functions, f_1 and f_2, on the unit disc with no common zeros, it is possible to find two other bounded analytic functions, g_1 and g_2, such that f_1g_1+f_2g_2=1. Moreover, the functions g_1 and g_2 can be chosen with some norm control. In this talk we will discuss what is known about the problem, some applications that arise from it, and an exciting new generalization of this result to certain function spaces on the unit ball in several complex variables.