Title: Harmonic Analysis Associated with the Generalized Weinstein Operator
Author(s): Ahmed Abouelaz, Azz-edine Achak, Radouan Daher, El Mehdi Loualid
Pages: 19-28
Cite as:
Ahmed Abouelaz, Azz-edine Achak, Radouan Daher, El Mehdi Loualid, Harmonic Analysis Associated with the Generalized Weinstein Operator, Int. J. Anal. Appl., 9 (1) (2015), 19-28.

Abstract


In this paper we consider a generalized Weinstein operator ∆d,α,n on Rd−1×]0,∞[, which generalizes the Weinstein operator ∆d,α, we define the generalized Weinstein intertwining operator Rα,n which turn out to be transmutation operator between ∆d,α,n and the Laplacian operator ∆d. We build the dual of the generalized Weinstein intertwining operatortRα,n, another hand we prove the formula related Rα,n andtRα,n . We exploit these transmutation operators to develop a new harmonic analysis corresponding to ∆d,α,n.

Full Text: PDF

 

References


  1. R. F. Al Subaie and M. A. Mourou, Transmutation Operators Associated with a Bessel Type Operator on The Half Line and Certain of Their Applications, Tamsui Oxford Journal of Information and Mathematical Sciences, 29(2013), 329-349.

  2. Hassen Ben Mohamed, Nèji Bettaibi, Sidi Hamidou Jah, Sobolev Type Spaces Asociated with the Weinstein Operator, Int. Journal of Math. Analysis, 5(2011), , 1353-1373.

  3. Hatem Mejjaoli, Ahsaa, Makren Salhi, Uncertainty Principles for the Weinstein transform, Czechoslovak Mathematical Journal, 61(2011), 941-974.

  4. Youssef Othmani and Khalifa Trimèche, Real Paley-Wiener Theorems Associated with the Weinstein Operator, Mediterr. J. Math. 3(2006), 105-118.