Potential fields with axial symmetry and algebras of monogenic functions of a vector variable. I

Abstract

We obtain a new representation of potential and flow functions for space potential solenoidal fields with axial symmetry. We study principal algebraic-analytical properties of monogenic functions of a vector variable with values in an infinite-dimensional Banach algebra of even Fourier series and describe the relationship between these functions and the axially symmetric potential and Stokes flow function. The suggested method for the description of the above-mentioned fields is an analog of the method of analytic functions in the complex plane for the description of plane potential fields.