Der Satz von Cauchy-Kowalewski für hyperanalytische Funktionen. (The Cauchy-Kowalewski Theorem for hyperanalytic functions) (Q1097394)

Let \({\mathcal D}_ r\) (r\(\geq 0)\) be the set of all regular upper triangular matrices with complex entries. Then, by definition, the hyperanalytic functions \(w=w(z_ 1,...,z_ n)\) are \({\mathcal D}_ r\)-valued functions, solutions of the system \(\partial w/\partial z\) \(*_ j+q_ j\partial w/\partial z_ j=0\) (1\(\leq j\leq n)\), where \(q_ j\) are arbitrary fixed \({\mathcal D}_ r\)-valued functions with Hölder-continuous derivatives. Using the common method of scales of Banach spaces, the existence and uniqueness of solutions of the Cauchy-Kowalewski problem in the area of the hyperanalytic functions is proved.