Tempered generalized functions and Hermite expansions |
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Authors: | Pedro Catuogno Christian Olivera |
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Institution: | Departamento de Matemática, Universidade Estadual de Campinas, 13.081-970, Campinas-SP, Brazil |
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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 Itô formula in this context and some applications to stochastic analysis. |
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Keywords: | 46F30 60H |
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