Fock and Hardy spaces: Clifford Appell case. Issue 5 (12th April 2022) - Alpay, Daniel; Diki, Kamal; Sabadini, Irene
Abstract: In this paper, we study a specific system of Clifford–Appell polynomials and, in particular, their product. Moreover, we introduce a new family of quaternionic reproducing kernel Hilbert spaces in the framework of Fueter regular functions. The construction is based on a general idea which allows us to obtain various function spaces by specifying a suitable sequence of real numbers. We focus on the Fock and Hardy cases in this setting, and we study the action of the Fueter mapping and its range.