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

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...

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Autor principal: OKA,YASUYUKI
Lenguaje:English
Publicado: Universidad de La Frontera. Departamento de Matemática y Estadística. 2010
Materias:
Weyl transform
Gel'fand-Shilov space
Fourier-Wigner transform
trace class operator
Schwartz's kernel theorem
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300015
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spelling oai:scielo:S0719-064620100003000152018-10-08On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual SpaceOKA,YASUYUKI Weyl transform Gel'fand-Shilov space Fourier-Wigner transform trace class operator Schwartz's kernel theorem 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.12 n.3 20102010-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300015en10.4067/S0719-06462010000300015
institution Scielo Chile
collection Scielo Chile
language English
topic Weyl transform
Gel'fand-Shilov space
Fourier-Wigner transform
trace class operator
Schwartz's kernel theorem
spellingShingle Weyl transform
Gel'fand-Shilov space
Fourier-Wigner transform
trace class operator
Schwartz's kernel theorem
OKA,YASUYUKI
On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual Space
description 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.
author OKA,YASUYUKI
author_facet OKA,YASUYUKI
author_sort OKA,YASUYUKI
title On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual Space
title_short On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual Space
title_full On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual Space
title_fullStr On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual Space
title_full_unstemmed On the Weyl Transform with Symbol in the Gel'fand-Shilov Space and its Dual Space
title_sort on the weyl transform with symbol in the gel'fand-shilov space and its dual space
publisher Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate 2010
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000300015
work_keys_str_mv AT okayasuyuki ontheweyltransformwithsymbolinthegel39fandshilovspaceanditsdualspace
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