Acta Mathematica Vietnamica
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The Dirichlet Problem Associated to Operators Defined on the Nuclear Algebra of Entire Functions
Sonia Chaari , Afef Ben Farahpp. 159-172
Abstract
This paper is devoted to the Dirichlet problem associated to operators defined on the nuclear algebra of entire functions. Firstly, we give a probabilistic representation of the solution of the Dirichlet problem associated to the extended $K$-Gross Laplacian in terms of $K$-Wiener process. Secondly, we prove that the Dirichlet problem associated to the operator $\mathcal {F}_{t(-K),I}$-transform has an explicit solution. Finally, an application to the large deviation principle is given.