versión On-line ISSN 0719-0646
OKA, YASUYUKI. On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual Space. Cubo [online]. 2010, vol.12, n.3, pp. 241-253. ISSN 0719-0646. http://dx.doi.org/10.4067/S0719-06462010000300015.
In this paper, we claim two subjects. One is that the Weyl transform with symbol in the Gel'fand-Shilov space l rr , r ≥ 1/2 , is a trace class operator. The other one is that the Weyl transform with symbol in the generalized function (l rr )1, r ≥ 1/2 , is a continuous linear transformation from the Gel'fand-Shilov space l rr to (l rr )1. As r > 1, Z. Lozanov- Crvenkovic and D. Periic have proved in  this result. Our second claim includes their result.
Palabras clave : Weyl transform; Gel'fand-Shilov space; Fourier-Wigner transform; trace class operator; Schwartz's kernel theorem.