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

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

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...

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Main Author: Privault, Nicolas
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2016
Subjects:
Weitzenböck identity
De Rham–Hodge–Kodaira decomposition
Online Access:https://hdl.handle.net/10356/84665
http://hdl.handle.net/10220/41915
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-846652023-02-28T19:33:24Z De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space Privault, Nicolas School of Physical and Mathematical Sciences Weitzenböck identity De Rham–Hodge–Kodaira decomposition 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. Accepted version 2016-12-21T06:10:51Z 2019-12-06T15:49:05Z 2016-12-21T06:10:51Z 2019-12-06T15:49:05Z 2016 Journal Article 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-. 0219-0257 https://hdl.handle.net/10356/84665 http://hdl.handle.net/10220/41915 10.1142/S0219025716500107 en Infinite Dimensional Analysis, Quantum Probability and Related Topics © 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]. 36 p. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Weitzenböck identity
De Rham–Hodge–Kodaira decomposition
spellingShingle Weitzenböck identity
De Rham–Hodge–Kodaira decomposition
Privault, Nicolas
De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Privault, Nicolas
format Article
author Privault, Nicolas
author_sort Privault, Nicolas
title De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space
title_short De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space
title_full De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space
title_fullStr De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space
title_full_unstemmed De Rham–Hodge decomposition and vanishing of harmonic forms by derivation operators on the Poisson space
title_sort de rham–hodge decomposition and vanishing of harmonic forms by derivation operators on the poisson space
publishDate 2016
url https://hdl.handle.net/10356/84665
http://hdl.handle.net/10220/41915
_version_ 1759855831829970944

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