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arXiv · 1604.05551

A Characterisation of the Euclidean Fourier transform on the Schwartz space

R. Lakshmi Lavanya
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Abstract

We obtain a characterisation of the Fourier transform on the space of Schwartz class functions on $\mathbb{R}^n.$ 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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R. Lakshmi Lavanya. 2016-04-19. A Characterisation of the Euclidean Fourier transform on the Schwartz space. https://arxiv.org/abs/1604.05551

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