Begehr, Heinrich Iterations of Pompeiu operators. (English) Zbl 0908.47048 Mem. Differ. Equ. Math. Phys. 12, 13-21 (1997). Summary: The Pompeiu operator \(T\) was extensively used by I. N. Vekua in his treatment of generalized Cauchy-Riemann systems. In the case of several complex variables when polydomains are considered, proper combinations of different \(T\)-operators for different components of the variable lead to a particular solution of the inhomogeneous Cauchy-Riemann system. This is applied to solve explicitely the Dirichlet problem in the unit polydisc for the inhomogeneous pluriharmonic system in the case of two complex variables. Cited in 14 Documents MSC: 47G10 Integral operators 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35C15 Integral representations of solutions to PDEs Keywords:Cauchy-Pompeiu representation; higher-order equations; boundary value problems; polydomains; Pompeiu operator; generalized Cauchy-Riemann systems; Dirichlet problem; inhomogeneous pluriharmonic system PDFBibTeX XMLCite \textit{H. Begehr}, Mem. Differ. Equ. Math. Phys. 12, 13--21 (1997; Zbl 0908.47048) Full Text: EuDML EMIS