A Characterisation of the Euclidean Fourier transform on the Schwartz space
Classical Analysis and ODEs
2016-04-20 v1
Abstract
We obtain a characterisation of the Fourier transform on the space of Schwartz class functions on The result states that any appropriately additive bijection of the Schwartz space onto itself, which interchanges convolution and pointwise products is essentially the Fourier transform.
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Cite
@article{arxiv.1604.05551,
title = {A Characterisation of the Euclidean Fourier transform on the Schwartz space},
author = {R. Lakshmi Lavanya},
journal= {arXiv preprint arXiv:1604.05551},
year = {2016}
}
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11 pages