On the Schwarz reflection principle for monogenic functions (Q2642857)

The paper under review is dedicated to generalizations of the classical Schwarz reflection principle to more general situations. A very nice introduction makes the reader familiar with the history of this kind of extension problems. With the help of methods of Clifford analysis the validity of a Schwarz type reflection principle for monogenic function is studied. After a brief introduction of elements of Clifford analysis Schwarz principles are investigated for the following situations: the \(\text{spin}(1)\) case, the \(\text{spin}(1/2)\) case, \(\mathbb{R}^m\), hyperplanes and \(S^m\). It should be noted that the \(\text{Spin}(1)\) case includes the Schwarz reflection principle for holomorphic functions in the plane.