Some Representations of Triharmonic Functions

Abstract

In this paper, a range of results have been obtained that enable one to consider the theory of game dynamics problems as an environment for constructing important mathematical objects. Namely, the triharmonic equation is integrated in the Cartesian coordinates with specially selected boundary conditions. The triharmonic Poisson integral for the upper half-plane, which belongs to the class of positive operators, is constructed. The functional dependence of the triharmonic operator on periodic functions is considered, and an integral with a delta-shaped kernel is obtained, which can be decomposed into three constant-sign fractions. The analysis of the asymptotic behavior of the triharmonic kernel shows the consistency of the obtained results with the previously known results. Keywords: triharmonic equation, upper half-plane, Fourier transform, Fourier series, positive operator.