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Adv. Pure Appl. Math. 3 (2012), 113–122 DOI 10.1515/APAM.2011.015 © de Gruyter 2012 A characterisation of the Weyl transform R. Lakshmi Lavanya and S. Thangavelu Abstract. A theorem of Alesker et al. says that the Fourier transform on Rn is essentially the only transform on the space of tempered distributions which interchanges convolutions and products. In this note we obtain a similar characterisation for the Weyl transform. Keywords. Schwartz class, tempered distributions, Weyl transform, Fourier–Weyl transform, noncommutative derivations. 2010 Mathematics