Representation of completely $L$-superharmonic functions

An infinitely differentiable function $u(x)$ is said to be completely $L$-superharmonic if it satisfies the condition $(-1)^nL^nu(x)\geqslant0$, $n=0,1,2,\dots$, where $L$ is a second-order elliptic operator and belongs to a bounded domain with a sufficiently smooth boundary. An integral representation is given in this paper for such functions, and a study of their analytic nature is carried out.
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