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

• 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
• Institution: Nanyang Technological University

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...