Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/84665
Title: De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space
Authors: Privault, Nicolas
Keywords: Weitzenböck identity
De Rham–Hodge–Kodaira decomposition
Issue Date: 2016
Source: Privault, N. (2016). De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 19(2), 1650010-.
Series/Report no.: Infinite Dimensional Analysis, Quantum Probability and Related Topics
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.
URI: https://hdl.handle.net/10356/84665
http://hdl.handle.net/10220/41915
ISSN: 0219-0257
DOI: 10.1142/S0219025716500107
Rights: © 2016 World Scientific Publishing Company. This is the author created version of a work that has been peer reviewed and accepted for publication by Infinite Dimensional Analysis, Quantum Probability and Related Topics, World Scientific Publishing Company. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1142/S0219025716500107].
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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