arXiv Analytics

Sign in

arXiv:1111.1295 [math.PR]AbstractReferencesReviewsResources

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

Yuxin Yang

Published 2011-11-05Version 1

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.

Journal: Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 16, No. 1 (2013)
Categories: math.PR, math.GN, math.RT
Subjects: 58A14, 58A12, 58B05, 20C35, 60H30
Related articles: Most relevant | Search more
arXiv:1409.5861 [math.PR] (Published 2014-09-20)
An extension of the Beckner's type Poincaré inequality to convolution measures on abstract Wiener spaces
arXiv:1608.07124 [math.PR] (Published 2016-08-25)
A representation for the Kantorovich--Rubinstein distance on the abstract Wiener space
arXiv:math/0312455 [math.PR] (Published 2003-12-25, updated 2007-12-20)
The divergence of Banach space valued random variables on Wiener space

Links

Toolbox