Fock and Hardy spaces: Clifford-Appell case

2020/11/06 by Alpay, Daniel, Diki, Kamal, Sabadini, Irene · 1 citation
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.03159

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 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.

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• Towards Fock Spaces in Hypercomplex Analysis

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