Acta Mathematica Vietnamica
- Volume 50
- Volume 49
- Volume 48
- Volume 47
- Volume 46
- Volume 45
- Volume 44
- Volume 43
- Volume 42
- Volume 41
- Volume 40
- Volume 39
- Volume 38
- Volume 37
- Volume 36
- Volume 35
- Volume 34
- Volume 33
- Volume 32
- Volume 31
- Volume 30
- Volume 29
- Volume 28
- Volume 27
- Volume 26
- Volume 25
- Volume 24
- Volume 23
- Volume 22
- Volume 21
- Volume 20
- Volume 19
- Volume 18
- Volume 17
- Volume 16
- Volume 15
- Volume 14
- Volume 13
- Volume 12
- Volume 11
- Volume 10
- Volume 9
- Volume 8
- Volume 7
- Volume 6
- Volume 5
- Volume 4
- Volume 3
- Volume 2
- Volume 1
The Dirichlet Problem Associated to Operators Defined on the Nuclear Algebra of Entire Functions
Sonia Chaari
,
Afef Ben Farah
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.