On polyharmonic Poisson-Taylor operators

In this paper, the Poisson operator is developed on the basis of solutions to polyharmonic equations. It is based on the triharmonic equation in Cartesian coordinates in the presence of classical boundary conditions. As a result, it is shown that the constructed triharmonic function is a sign-changing operator. The integral kernel of the triharmonic Poisson integral in the upper half-plane changes its sign twice within the definition domain. The triharmonic Poisson-Taylor operator discovered in the paper is determined by the Taylor formulas for two different integrals that form the triharmonic function.