Harmonic Analysis Associated with the Generalized Weinstein Operator

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Ahmed Abouelaz
Azz-edine Achak
Radouan Daher
El Mehdi Loualid

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.

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References

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