Ito-Wiener chaos and the Hodge decomposition on an abstract Wiener space

Details Ito-Wiener chaos and the Hodge decomposition on an abstract Wiener space Ito-Wiener chaos and the Hodge decomposition on an abstract Wiener space

2011-11-05

arxiv.org/abs/1111.1295v1

Mathematics

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Using the structure of the Boson-Fermion Fock space and an argument taken from [2], we give a new proof of the triviality of the $L^2$ cohomology groups on an abstract Wiener space, alternative to that given by Shigekawa [9]. We apply some representation theory of the symmetric group to characterise the spaces of exact and co-exact forms in their Boson-Fermion Fock space representation.

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