2024/09/06 by Rolf Sören Kraußhar, Kraußhar, Rolf Sören, Anastasiia Legatiuk +3
Computer Science · Mathematics · #39A12 #42A38 #44A15 #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2409.04285
openalex publication_date 2024/09/06 · openalex created_date 2024/10/21 · openalex updated_date 2026/07/28
In this paper, we finish the basic development of the discrete octonionic analysis by presenting a Weyl calculus-based approach to bounded domains in ℝ8. In particular, we explicitly prove the discrete Stokes formula for a bounded cuboid, and then we generalise this result to arbitrary bounded domains in interior and exterior settings by the help of characteristic functions. After that, discrete interior and exterior Borel-Pompeiu and Cauchy formulae are introduced. Finally, we recall the construction of discrete octonionic Hardy spaces for bounded domains. Moreover, we explicitly explain where the non-associativity of octonionic multiplication is essential and where it is not. Thus, this paper completes the basic framework of the discrete octonionic analysis introduced in previous papers, and, hence, provides a solid foundation for further studies in this field.