Bulletin of the
Korean Mathematical Society BKMS

In recent years, the study of slice Dirac operators has attracted more and more attention in the literature. In this paper, Almansi-type decompositions for null solutions to the iterated slice Dirac operator and the generalized slice Dirac operator are obtained without a star-like domain centered at the origin. As applications, we investigate Riquier type problems and Dirichlet type problems in the theory of slice monogenic functions.

Keywords: slice Dirac operator, Euler operator, generalized slice Dirac operator, Riquier problem, Dirichlet problem

MSC numbers: 30G35, 30E25, 35G15