On the Weyl transform with symbol in the Gel‘fand-Shilov space and its dual space

Yasuyuki Oka

doi:10.4067/S0719-06462010000300015

On the Weyl transform with symbol in the Gel‘fand-Shilov space and its dual space

Authors

Yasuyuki Oka Department of Mathematics, Sophia University 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan.

DOI:

https://doi.org/10.4067/S0719-06462010000300015

Keywords:

Weyl transform, Gel‘fand-Shilov space, Fourier-Wigner transform, trace class operator, Schwartz‘s kernel theorem

Abstract

In this paper, we claim two subjects. One is that the Weyl transform with symbol in the Gel‘fand-Shilov space , is a trace class operator. The other one is that the Weyl transform with symbol in the generalized function , is a continuous linear transformation from the Gel‘fand-Shilov space to . As r > 1, Z. Lozanov-CrvenkoviÄ‡ and D. PerišiÄ‡ have proved in [6] this result. Our second claim includes their result.