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

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DOI:

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

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-Crvenković and D. Perišić have proved in [6] this result. Our second claim includes their result.

Keywords

Weyl transform , Gel‘fand-Shilov space , Fourier-Wigner transform , trace class operator , Schwartz‘s kernel theorem
  • Yasuyuki Oka Department of Mathematics, Sophia University 7-1 Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan.
  • Pages: 241–253
  • Date Published: 2010-10-01
  • Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal

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Published

2010-10-01

How to Cite

[1]
Y. Oka, “On the Weyl transform with symbol in the Gel‘fand-Shilov space and its dual space”, CUBO, vol. 12, no. 3, pp. 241–253, Oct. 2010.

Issue

Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal

Section

Articles