Cauchy formulae and Hardy spaces in discrete octonionic analysis

2023/05/06 by Kraußhar, Rolf Sören, Legatiuk, Dmitrii
#39A12 #42A38 #44A15 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.04121

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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