1. Laplace operators in gamma analysis
- Author
-
Hagedorn, D., Kondratiev, Y., Lytvynov, E., and Vershik, A.
- Subjects
Mathematics - Probability ,Primary 60G51, 60G55, 60G57, Secondary 60G20, 60H40 - Abstract
Let $\mathbb K(\mathbb R^d)$ denote the cone of discrete Radon measures on $\mathbb R^d$. The gamma measure $\mathcal G$ is the probability measure on $\mathbb K(\mathbb R^d)$ which is a measure-valued L\'evy process with intensity measure $s^{-1}e^{-s}\,ds$ on $(0,\infty)$. We study a class of Laplace-type operators in $L^2(\mathbb K(\mathbb R^d),\mathcal G)$. These operators are defined as generators of certain (local) Dirichlet forms. The main result of the papers is the essential self-adjointness of these operators on a set of `test' cylinder functions on $\mathbb K(\mathbb R^d)$.
- Published
- 2014