Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 74, Issue 2, Pages 479-493Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2010.09.003
Keywords
Hermite functions; Generalized function algebras; Fourier transform; Ito formula
Categories
Funding
- CNPQ [302704/2008-6]
- FAPESP [2007/54740-4]
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In this work we introduce an algebra of tempered generalized functions. The tempered distributions are embedded in this algebra via their Hermite expansions. The Fourier transform is naturally extended to this algebra in such a way that the usual relations involving multiplication, convolution and differentiation are valid. Furthermore, we give a generalized Ito formula in this context and some applications to stochastic analysis. (C) 2010 Elsevier Ltd. All rights reserved.
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