On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual Space

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...

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Bibliographic Details
Published in:Cubo (Temuco, Chile) Chile), 2010, Vol.12 (3), p.241-253
Main Author: OKA, YASUYUKI
Format: Article
Language:English
Subjects:
Fourier-Wigner transform
Gel'fand-Shilov space
MATHEMATICS
MATHEMATICS, APPLIED
Schwartz's kernel theorem
trace class operator
Weyl transform
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Summary: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.
ISSN:0719-0646
0716-7776
0719-0646
DOI:10.4067/S0719-06462010000300015