Hadamard three-hyperballs type theorem and overconvergence of special monogenic simple series (Q2019116)

The title explains the goal of the work, and a brief Section 1 ``Introduction'' gives some motivation of it. Section 2 ``Preliminaries'' deals with basic notions of Clifford analysis and with the notion of special monogenic polynomial series and their properties; monogenic means, as always, null solutions of the Cauchy-Riemann operator of Clifford analysis. In Section 3 ``Hadamard three-circle theorem and generalizations'', first, some comments on the original version of the theorem and on generalizations for, e.g., subharmonic functions in \(\mathbb R^m\) are given. Second, a Hadamard three-hyperball type theorem is proved and its application to a property of all Cannon bases of special monogenic polynomials is shown. What is done in Section 4 is seen from its title ``Overconvergence of special monogenic simple series''; what here exactly means ``special'' and ``simple'' is explained previously.