Tempered Generalized Functions and Hermite Expansions
Functional Analysis
2010-07-01 v1 Probability
Abstract
In this work we introduce a new 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. We study the elementary properties of the association, embedding, point values and Fourier transform. Furthermore, we give a generalized Ito formula in this context and some applications to stochastic analysis.
Cite
@article{arxiv.1006.5862,
title = {Tempered Generalized Functions and Hermite Expansions},
author = {P. Catuogno and C. Olivera},
journal= {arXiv preprint arXiv:1006.5862},
year = {2010}
}