2023/11/14 by Kuzmenko, Tetiana, Shpakivskyi, Vitalii
#Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Operator Algebras (math.OA) #Primary 30G35 #Secondary 32A10
paper · doi:10.48550/arxiv.2311.08522
In the algebra of complex quaternions \mathbbH(C) we consider for the first time left- and right-ψ-hyperholomorphic functions. We justify the transition in left- and right-ψ-hyperholomorphic functions to a simpler basis i.e. to the Cartan basis. Using Cartan's basis we find the solution of Cauchy-Fueter equation. By the same method we find a representation of left-ψ-hyperholomorphic function in a special case.