On the convergence properties of basic series representing special monogenic functions (Q1423761)

The paper deals with the approximation of the class of ``special'' monogenic functions by polynomials. Monogenic functions are differentiable functions in the kernel of the Cauchy differential operator in a Clifford algebra. There are defined special monogenic polynomials and it is discussed the question, for which space of special monogenic functions these polynomials are a basis? There are obtained approximation results for polynomial basic sets that are a Cannon set. These Cannon basic sets reflect a certain regularity property of the polynomials in the set.