Formulations of the -functional calculus and some consequences. Issue 3 (5th May 2016) - Colombo, Fabrizio; Gantner, Jonathan
Abstract : In this paper we introduce the two possible formulations of the -functional calculus that are based on the Fueter–Sce mapping theorem in integral form and we introduce the pseudo- -resolvent equation. In the case of dimension 3 we prove the -resolvent equation and we study the analogue of the Riesz projectors associated with this calculus. The case of dimension 3 is also useful to study the quaternionic version of the -functional calculus.