Reproducing inversion formulas for the Dunkl-Wigner transforms

• Fethi Soltani ^[1]
  1. [1] Jazan University

     Jazan University

     Arabia Saudí

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 17, Nº. 2, 2015, págs. 1-14
• Idioma: inglés
• DOI: 10.4067/S0719-06462015000200001
• Enlaces
  • Texto completo
• Resumen
  • español

    Definimos y estudiamos la transformada de Fourier-Wigner asociada a los operadores de Dunkl, y probamos una fórmula de inversion y una formula de Plancherel para esta transformada. Luego introducimos y estudiamos las funciones extramales asociadas a la transformada de Dunkl-Wigner.

  • English

    We define and study the Fourier-Wigner transform associated with the Dunkl operators, and we prove for this transform a reproducing inversion formulas and a Plancherel formula. Next, we introduce and study the extremal functions associated to the Dunkl- Wigner transform

• Referencias bibliográficas
  • Dachraoui, A. (2001). Weyl-Bessel transforms. J. Comput. Appl. Math. 133. 263-276
  • Dunkl, C.F. (1991). Integral kernels with reflection group invariance. Canad. J. Math. 43. 1213-1227
  • Dunkl, C.F. (1992). Hankel transforms associated to finite reflection groups. Contemp. Math. 138. 123-138
  • de Jeu, M.F.E. (1993). The Dunkl transform. Invent. Math. 113. 147-162
  • Kimeldorf, G.S,Wahba, G. (1971). Some results on Tchebycheffian spline functions. J. Math. Anal. Appl. 33. 82-95
  • Matsuura, T,Saitoh, S,Trong, D.D. (2005). Inversion formulas in heat conduction multidimensional spaces. J. Inv. Ill-posed Problems. 13. 479-493
  • Opdam, E.M. (1993). Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group. Compositio Math. 85. 333-373
  • Rösler, M. (1999). Positivity of Dunkl’s intertwining operator. Duke Math. J. 98. 445-463
  • Rösler, M. (2003). A positive radial product formula for the Dunkl kernel. Trans. Amer. Math. Soc. 355. 2413-2438
  • Saitoh, S. (1983). Hilbert spaces induced by Hilbert space valued functions. Proc. Amer. Math. Soc. 89. 74-78
  • Saitoh, S. (1983). The Weierstrass transform and an isometry in the heat equation. Appl. Anal. 16. 1-6
  • Saitoh, S. (2004). Approximate real inversion formulas of the Gaussian convolution. Appl. Anal. 83. 727-733
  • Saitoh, S. (2005). Best approximation, Tikhonov regularization and reproducing kernels. Kodai Math. J. 28. 359-367
  • Soltani, F. (2005). Inversion formulas in the Dunkl-type heat conduction on d. Appl. Anal. 84. 541-553
  • Soltani, F. (2012). Best approximation formulas for the Dunkl L²-multiplier operators ond. Rocky Mountain J. Math. 42. 305-328
  • Soltani, F. (2013). Multiplier operators and extremal functions related to the dual Dunkl-Sonine operator. Acta Math. Sci. 33. 430-442
  • Soltani, F. (2014). Uncertainty principles and extremal functions for the Dunkl L²-multiplier operators. J. Oper. 2014. 1-9
  • Thangavelu, S,Xu, Y. (2005). Convolution operator and maximal function for the Dunkl transform. J. Anal. Math. 97. 25-55
  • Thangavelu, S,Xu, Y. (2007). Riesz transform and Riesz potentials for Dunkl transform. J. Comput. Appl. Math. 199. 181-195
  • Yamada, M,Matsuura, T,Saitoh, S. (2007). Representations of inverse functions by the integral transform with the sign kernel. Frac. Calc....
  • Weyl, H. (1950). The theory of groups and quantum mechanics. Dover. New York.
  • Wong, M.W. (1998). Weyl transforms. Universitext, Springer. New York.