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In this paper, we study the Bargmann–Radon transform and a class of monogenic functions called axially monogenic functions. First, we compute the explicit formula of the Bargmann–Radon transform for axially monogenic functions, by making use of the Funk–Hecke theorem. Then we present the explicit form of the general Cauchy–Kowalewski extension for radial function. Finally, by making use of the results we obtained, we give an application of the Bargmann–Radon transform for Cauchy–Kowalewski extension. [ABSTRACT FROM AUTHOR]

In this paper, we study a refinement of the Szegö-Radon transform in the hypermonogenic setting. Hypermonogenic functions form a subclass of monogenic functions arising in the study of a modified Dirac operator, which allows for weaker symmetries and also has a strong connection to the hyperbolic metric. In particular, we construct a projection operator from a module of hypermonogenic functions in R p + q onto a suitable submodule of plane waves parameterized by a vector on the unit sphere of R q. Moreover, we study the interaction of this Szegö-Radon transform with the generalized Cauchy-Kovalevskaya extension operator. Finally, we develop a reconstruction (inversion) method for this transform. [ABSTRACT FROM AUTHOR]