A Characterisation of the Euclidean Fourier transform on the Schwartz   space
  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. 
R. Lakshmi Lavanya
math.CA