2010/06/30 by Pedro Catuogno, P. Catuogno, Catuogno, P. +3
Mathematics · Physics and Astronomy · #46F30 #60H #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Mathematical and Theoretical Analysis #Probability (math.PR) #Statistical Mechanics and Entropy #math.FA #math.PR #msc:46F30 #msc:60H
paper · pdf · doi:10.48550/arxiv.1006.5862
arxiv created 2010/06/30 · openalex publication_date 2010/06/30 · arxiv updated 2010/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.