Ir al contenido

Documat


Uncertainty principle for the Riemann-Liouville operator

  • Khaled Hleili [1] ; Slim Omri [2] ; Lakhdar T Rachdi [3]
    1. [1] Institut national des sciences appliquees et de Thechnologie Faculty of Applied Mathematics Departement de Mathematiques et d’Informatique
    2. [2] Institut preparatoire aux etudes d’ingenieurs Departement de Mathematiques Appliquees
    3. [3] Faculte des Sciences de Tunis Departement de Math ematiques
  • Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 13, Nº. 3, 2011, págs. 91-115
  • Idioma: inglés
  • DOI: 10.4067/S0719-06462011000300006
  • Enlaces
  • Resumen
    • español

      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.

    • English

      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.

  • Referencias bibliográficas
    • Andrews, G.,Askey, R.,Roy, R.. (1999). Special Functions.
    • Baccar, C.,Hamadi, N. B.,Rachdi, L. T.. (2006). Inversion formulas for the Riemann-Liouville transform and its dual associated with singular...
    • Farah, S. Ben,Mokni, K.. (2003). Uncertainty Principle and the (Lp, Lq) version of Morgans theorem on some groups. Russ. J. Math. Phys.. 10....
    • Beurling, A.. (1989). The collected works of Arne Beurling. 12.
    • Bonami, A.,Demange, B.,Jaming, P.. (2003). Hermite functions and uncertainty priciples for the Fourier and the widowed Fourier transforms....
    • Bouattour, L.,Trimeche, K.. (2005). An analogue of the Beurling-Hormander's theorem for the Chebli-Trimeche transform. Glob. J. Pure Appl....
    • Chabat, B.. (1985). Introduction a l'analyse complexe. Edition Mir. Moscou.
    • Cowling, M.G.,Price, J. F.. (1983). Generalizations of Heisenbergs inequality in Harmonic analysis. (Cortona, 1982), Lecture Notes in Math.,....
    • Erdely, A.,all. (1956). Asymptotic expansions. Dover publications. New-York.
    • Erdely, A.,all. (1954). Tables of integral transforms. Mc Graw-Hill Book Compagny. New York.
    • Folland, G. B.. (1984). Real Analysis Modern Techniques and Their Applications. John Wiley and Sons.. New York.
    • Folland, G. B.,Sitaram, A.. (1997). The uncertainty principle: a mathematical survey. J. Fourier Anal. Appl.. 3. 207-238
    • Gelfand, I.M.,Shilov, G.E.. (1953). Fourier transforms of rapidly increasing functions and questions of uniqueness of the solution of Cauchy's...
    • Hardy, G. H.. (1933). A theorem concerning Fourier transform. J. London. Math. Soc.. 8. 227-231
    • Havin, V.,Joricke, B.. (1994). An uncertainty principle in harmonic analysis.
    • Hormander, L.. (1991). A uniqueness theorem of Beurling for Fourier transform pairs. Ark. Mat.. 29. 237-240
    • Kamoun, L.,Trimeche, K.. (2005). An Analogue of Beurling-Hormander's Theorem Associated with Partial Differential Operators. Meditter....
    • Lebedev, N. N.. (1972). Special Functions and their applications. Dover publications. New-York.
    • Morgan, G. W.. (1934). A note on Fourier transforms. J. London. Math. Soc.. 9. 178-192
    • Omri, S.,Rachdi, L. T.. (2007). An Lp - Lq version of Morgan's theorem associated with Riemann-Liouville transform. Int. J. Math. Anal.....
    • Omri, S.,Rachdi, L. T.. (2008). Heisenberg-Pauli-Weyl uncertainty principle for the Riemann-Liouville Operator. J. Ineq. Pure and Appl. Math.....
    • Trimeche, K.. (2006). Beurling-Hormander's theorem for the Dunkl transform. Glob. J. Pure Appl. Math.. 2. 181-196
    • Trimeche, K.. (1997). Inversion of the Lions translation operator using genaralized wavelets. Appl. Comput. Harmonic Anal.. 4. 97-112
    • Trimeche, K.. (1981). Transformation integrale de Weyl et theoreme de Paley-Wienner associes a un operateur differentiel singulier sur (0,...
    • Watson, G. N.. (1959). A treatise on the theory of Bessel functions. Cambridge univ. Press2nd ed. Cambridge.
    • Yakubovich, S.B.. (2008). Uncertainty principles for the Kontorovich-Lebedev transform. Math. Mod- ell. Anal.. 13. 289-302
Los metadatos del artículo han sido obtenidos de SciELO Chile

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno