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arXiv · 2305.04121

Cauchy formulae and Hardy spaces in discrete octonionic analysis

Rolf Sören Kraußhar·Dmitrii Legatiuk
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Abstract

In this paper, we continue the development of a fundament of discrete octonionic analysis that is associated to the discrete first order Cauchy-Riemann operator acting on octonions. In particular, we establish a discrete octonionic version of the Borel-Pompeiu formula and of Cauchy's integral formula. The latter then is exploited to introduce a discrete monogenic octonionic Cauchy transform. This tool in hand allows us to introduce discrete octonionic Hardy spaces for upper and lower half-space together with Plemelj projection formulae.

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Rolf Sören Kraußhar, Dmitrii Legatiuk. 2023-05-06. Cauchy formulae and Hardy spaces in discrete octonionic analysis. https://arxiv.org/abs/2305.04121

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