Tempered generalized functions and Hermite expansions

Catuogno, Pedro; Olivera, Christian

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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Tempered generalized functions and Hermite expansions

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Author(s):	Catuogno, Pedro ^[1] ; Olivera, Christian ^[1] Total Authors: 2
Affiliation:	^[1] Univ Estadual Campinas, Dept Matemat, BR-13081970 Campinas, SP - Brazil Total Affiliations: 1
Document type:	Journal article
Source:	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 74, n. 2, p. 479-493, JAN 15 2011.
Web of Science Citations:	7
Abstract
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. (AU)

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