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De Rham-Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space.
- Source :
-
Infinite Dimensional Analysis, Quantum Probability & Related Topics . Jun2016, Vol. 19 Issue 2, p-1. 34p. - Publication Year :
- 2016
-
Abstract
- We construct differential forms of all orders and a covariant derivative together with its adjoint on the probability space of a standard Poisson process, using derivation operators. In this framewok we derive a de Rham-Hodge-Kodaira decomposition as well as Weitzenböck and Clark-Ocone formulas for random differential forms. As in the Wiener space setting, this construction provides two distinct approaches to the vanishing of harmonic differential forms. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02190257
- Volume :
- 19
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Infinite Dimensional Analysis, Quantum Probability & Related Topics
- Publication Type :
- Academic Journal
- Accession number :
- 116145617
- Full Text :
- https://doi.org/10.1142/S0219025716500107