| Abstrakt: |
The author has obtained the results that make it possible to consider the theory of dynamic game problems as an environment for constructing important mathematical objects. Namely, the triharmonic equation in the Cartesian coordinates with specially selected boundary conditions has been integrated. A triharmonic Poisson integral for the upper half-plane, which belongs to the class of positive operators, has been constructed. The functional dependence of the triharmonic operator on periodic functions has been considered, and an integral with the delta-shaped kernel has been obtained, which can be decomposed into three fractions of constant sign. The analysis of the asymptotic behavior of the triharmonic kernel shows the consistency of the obtained results with the already known results. [ABSTRACT FROM AUTHOR] |
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