Fock and Hardy spaces: Clifford-Appell case

Daniel Alpay; Kamal Diki; Irene Sabadini

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arXiv · 2011.03159

Fock and Hardy spaces: Clifford-Appell case

Daniel Alpay·Kamal Diki·Irene Sabadini

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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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Daniel Alpay, Kamal Diki, Irene Sabadini. 2020-11-06. Fock and Hardy spaces: Clifford-Appell case. https://arxiv.org/abs/2011.03159

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