Fock and Hardy spaces: Clifford Appell case. Issue 5 (12th April 2022)

• Record Type: Journal Article
• Authors: Alpay, Daniel; Diki, Kamal; Sabadini, Irene
• Is Part Of: Mathematische Nachrichten. Volume 295:Issue 5(2022)
• Page Start: 834
• Page End: 860
• Publication Date: 2022-04-12
• Subjects: Appell system -- Fock space -- Fueter mapping -- Hardy space -- hypercomplex derivative -- quaternions -- reproducing kernels -- shift operator; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.202000359
• Languages: English
• ISSNs: 0025-584X

Abstract

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.