5 citations · 17 across the 23 of their papers we have counts for
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Riesz transform and Riesz potentials for Dunkl transform
Sundaram Thangavelu, Yuan Xu
Analogous of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weighted functions that are invariant under a reflect…
Second order difference equations and discrete orthogonal polynomials of two variables
Yuan Xu
The second order partial difference equation of two variables $ \CD u:= A_{1,1}(x) Δ_1 \nabla_1 u + A_{1,2}(x) Δ_1 \nabla_2 u + A_{2,1}(x) Δ_2 \nabla_1 u + A_{2,2}(x) Δ_2 \nabla_2…
Convolution operator and maximal function for Dunkl transform
Sundaram Thangavelu, Yuan Xu
For a family of weight functions, , invariant under a finite reflection group on $\RR^d$, analysis related to the Dunkl transform is carried out for the weighted spaces.…
Generalized translation operator and approximation in several variables
Yuan Xu
Generalized translation operators for orthogonal expansions with respect to families of weight functions on the unit ball and on the standard simplex are studied. They are used to…
On polynomials of least deviation from zero in several variables
Yuan Xu
A polynomial of the form , where the degree of is less than the total degree of , is said to be least deviation from zero if it has the smallest uniform norm am…
On discrete orthogonal polynomials of several variables
Yuan Xu
Let be a set of isolated points in $\RR^d$. Define a linear functional $\CL$ on the space of real polynomials restricted on , $\CL f = \sum_{x \in V} f(x)ρ(x)$, where is…