On operators and elementary functions in Clifford analysis
This is an interesting article regarding regular functions in Clifford analysis. Elements from the Clifford algebra of the form \(x_0 + \underline{x}\) with \(x_0 \in\mathbb{R}\) and \(\underline{x} \in\mathbb{R}^n\) are called paravectors. For these paravectors as arguments the classical elementary functions are defined and Moivre's formulas are shown. Then the Cauchy-Fueter operator is decomposed into scalar and spherical terms, and some relations for these operators and paravector valued functions are proved. In the last chapter the Fueter map for regular functions \(\tau_n = \kappa_n\Delta^{\frac{n-1}{2}}\) where \(\kappa_n\) is a normalization factor, is used to get representations and properties for the elementary functions.
scientific article; zbMATH DE number 1331703
scientific article