2014/06/19 by Fabrizio Colombo, Colombo, Fabrizio, Roman Lavicka +5
Mathematics · #30G35 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30G35
paper · pdf · doi:10.48550/arxiv.1406.5019
arxiv created 2014/06/19 · arxiv updated 2014/06/20
In [J. Bures, R. Lavicka, V. Soucek, Elements of quaternionic analysis and Radon transform, Textos de Matematica 42, Departamento de Matematica, Universidade de Coimbra, 2009], the authors describe a link between holomorphic functions depending on a parameter and monogenic functions defined on R^(n+1) using the Radon and dual Radon transforms. The main aim of this paper is to further develop this approach. In fact, the Radon transform for functions with values in the Clifford algebra Rn is mapping solutions of the generalized Cauchy-Riemann equation, i.e., monogenic functions, to a parametric family of holomorphic functions with values in Rn and, analogously, the dual Radon transform is mapping parametric families of holomorphic functions as above to monogenic functions. The parametric families of holomorphic functions considered in the paper can be viewed as a generalization of the so-called slice monogenic functions. An important part of the problem solved in the paper is to find a suitable definition of the function spaces serving as the domain and the target of both integral transforms.