On the Dirichlet problem for invariant elliptic Dezin systems. (Q1595498)

The author obtains a number of new properties of invariant Dezin elliptic systems [\textit{A. A. Dezin}, Multi-dimensional analysis and discrete models (Russian), Nauka, Moskva (1990; Zbl 0704.39005)], using the matrix representation of these systems in \(\mathbb R^n\). In particular, in the case \(n=2\), one has the Cauchy-Riemann system, and in the case \(n=3\), the Moisil-Teodorescu-Bitsadze system. The solutions of invariant systems have many properties similar to the properties of holomorphic functions (e.g., theorems of Cauchy and Morera type, and the symmetry principle). Using the symmetry principle, the author obtains an integral representation of the solution of Dezin's system in the half-space \(x_1>0\) and finds the solution of the Dirichlet problem in this half-space.