Resumen

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.  doi: 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 ^r_r , r ≥ 1/2 , is a trace class operator. The other one is that the Weyl transform with symbol in the generalized function (l ^r_r )^1, r ≥ 1/2 , is a continuous linear transformation from the Gel'fand-Shilov space l ^r_r to (l ^r_r )¹. As r > 1, Z. Lozanov- Crvenkovic and D. Perišic have proved in [6] 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.