2018/12/18 by Alpay, Daniel, Paiva, Ismael L., Struppa, Daniele C.
#30G35 #46C20 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1812.07133
We develop some aspects of the theory of hyperholomorphic functions whose values are taken in a Banach algebra over a field -- assumed to be the real or the complex numbers -- and which contains the field. Notably, we consider Fueter expansions, Gleason's problem, the theory of hyperholomorphic rational functions, modules of Fueter series, and related problems. Such a framework includes many familiar algebras as particular cases. The quaternions, the split quaternions, the Clifford algebras, the ternary algebra, and the Grassmann algebra are a few examples of them.