Gleason’s problem associated to the fractional cauchy-riemann operator, fueter series, drury-arveson space and related topics

Abstract

In this paper we present the building blocks for a function theory based on fractional Cauchy-Riemann operators. We are going to construct basic monogenic powers and Fueter series. With these tools we are going to study Gleason’s problem and reproducing kernel spaces, like the Drury- Arveson space and de Branges-Rovnyak spaces. We end with a statement on Schur multipliers in this setting.