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.