  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 R_n is mapping solutions of the generalized
Cauchy-Riemann equation, i.e., monogenic functions, to a parametric family of
holomorphic functions with values in R_n 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.
