On a mean value property associated with the dunkl laplacian operator and applications

By H. Mejjaoli, Khalifa Trimeche. 2001

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Paley-Wiener Theorems for the Dunkl Transform and Dunkl Translation Operators (2002, methodology): “(iii) Using Dunkl translation operators tx, x 2 R , we study in [16] a mean value property associated with the Dunkl Laplacian operator Dk given by Dk 1⁄4 Xd j1⁄41 T(2) j : ð96Þ”
Uncertainty principles for the Dunkl transform (2010, unknown): “([16]) For u ∈ C(R) and x0 ∈ R, it follows that M r,x0(u) = n ∑”
Positive $$L^p$$Lp-Bounded Dunkl-Type Generalized Translation Operator and Its Applications (2017, background): “To overcome this difficulty, the spherical mean value of the translation operator τ y was introduced in [28] and it was studied in [42], where, in particular, its positivity was shown.”