Infinitesimal Fourier Transformation for The Space of Functionals

Details Infinitesimal Fourier Transformation for The Space of Functionals Infinitesimal Fourier Transformation for The Space of Functionals

2004-05-13

arxiv.org/abs/math/0405244v1

Mathematics

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Scientific paper

The purpose is to formulate a Fourier transformation for the space of functionals, as an infinitesimal meaning. We extend ${\bf R}$ to $ ^{\star}(^{\ast}{\bf R})$ under the base of nonstandard methods for the construction. The domain of a functional is the set of all internal functions from a $ ^{\ast}$-finite lattice to a $ ^{\ast}$-finite lattice with a double meaning. Considering a $ ^{\ast}$-finite lattice with a double meaning, we find how to treat the domain for a functional in our theory of Fourier transformation, and calculate two typical examples.

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