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In [J. Bures, R. Lavicka, V. Soucek, Elements of quaternionic analysis andRadon transform, Textos de Matematica 42, Departamento de Matematica,Universidade de Coimbra, 2009], the authors describe a link between holomorphicfunctions 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 tofurther develop this approach. In fact, the Radon transform for functions withvalues in the Clifford algebra R_n is mapping solutions of the generalizedCauchy-Riemann equation, i.e., monogenic functions, to a parametric family ofholomorphic functions with values in R_n and, analogously, the dual Radontransform is mapping parametric families of holomorphic functions as above tomonogenic functions. The parametric families of holomorphic functionsconsidered in the paper can be viewed as a generalization of the so-calledslice monogenic functions. An important part of the problem solved in the paperis to find a suitable definition of the function spaces serving as the domainand the target of both integral transforms.

The Radon transform between monogenic and generalized slice monogenic functions