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arXiv · 1006.5862

Tempered Generalized Functions and Hermite Expansions

P. Catuogno·C. Olivera
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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.

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P. Catuogno, C. Olivera. 2010-06-30. Tempered Generalized Functions and Hermite Expansions. https://arxiv.org/abs/1006.5862

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