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versão ISSN 0719-0646

Cubo vol.13 no.3 Temuco out. 2011

doi: 10.4067/S0719-06462011000300006

CUBO A Mathematical Journal Vol.13, NQ03, (91-115). October 2011

Uncertainty principle for the Riemann-Liouville operator

Hleili Khaled, Omri Slim and Lakhdar T. Rachdi

Faculty of Applied Mathematics,Departement de Mathematiques et d'Informatique, Institut national des sciences appliquees et de Thechnologie, Centre Urbain Nord BP 676 - 1080 Tunis cedex, Tunisia, email: khaled.hleili@gmail.com

Departement de Mathematiques Appliquees, Institut preparatoire aux (etudes d'ingenieurs, Campus universitaire Mrezka - 8000 Nabeul, Tunisia. email: slim.omri@issig.rnu.tn

Departement de Math ematiques, Faculte des Sciences de Tunis, 2092 El Manar II, Tunisia. email: lahhdartannech.rachdi@fst.rnu.tn

ABSTRACT

A Beurling-Hormander theorem's is proved for the Fourier transform connected with the Riemann-Liouville operator. Nextly, Gelfand-Shilov and Cowling-Price type theorems are established.

Keywords: Beurling-Hormander theorem, Gelfand-Shilov theorem, Cowling- Price theorem, Fourier transform, Riemann-Liouville operator.

Mathematics Subject Classification: 43A32; 42B10.

RESUMEN

Se demuestra el teorema de Beurling-Hormander por la transformada de Fourier conectada con el operador de Riemann-Liouville. Ademas, se establecen teoremas tipo de Gelfand-Shilov y Cowling-Price.

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Received: July 2010. Revised: August 2010.