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1. De Rham-Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space.

Author

Privault, Nicolas

Subjects
*MATHEMATICAL decomposition, *HARMONIC analysis (Mathematics), *POISSON algebras, *HARMONIC spaces (Mathematics), *COVARIANT canonical quantization
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]

Published
2016
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