On the convergence properties of basic series representing Clifford valued functions (Q1864308)

The authors consider the class of so-called special monogenic functions over an inner domain in \(\mathbb{R}^{n+1}\). An arbitrary function \(f\) is defined by \[ f(x)= \sum^\infty_{n=0} z_n(x)c_n\quad c_n\in Cl_{0,m} \] with \[ z_n(x)=\sum_{r+j=n} \frac{\bigl((m-1)/2)_i (m+1/2)_j}{i!j!} \overline x^ix^j. \] There are studied the convergence properties of a basic series representing entire special monogenic functions. The authors have formulated conditions under which a polynomial system \(\{P_n\}\), which consist of \(Cl_{0,m}\) linear combinations of \(z_k\), forms a Cannon set.