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Symmetries of slice monogenic functions. (English) Zbl 1468.30083

Summary: In this paper we consider the symmetry behavior of slice monogenic functions under Möbius transformations. We describe the group under which slice monogenic functions are taken into slice monogenic functions. We prove a transformation formula for composing slice monogenic functions with Möbius transformations and describe their conformal invariance. Finally, we explain two construction methods to obtain automorphic forms in the framework of this function class. We round off by presenting a precise algebraic characterization of the subset of slice monogenic linear fractional transformations within the set of general Möbius transformations.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
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