5 citations · 9 across the 10 of their papers we have counts for
10 papers · 1 filter
Localized polynomial frames on the interval with Jacobi weights
Pencho Petrushev, Yuan Xu
As is well known the kernel of the orthogonal projector onto the polynomials of degree in $L^2(w_{\a,\b}, [-1, 1])$ with $w_{\a,\b}(t) = (1-t)^\a(1+t)^\b$ can be written in ter…
A family of Sobolev Orthogonal Polynomials on the Unit Ball
Yuan Xu
A family of orthonormal polynomials on the unit ball of $\RR^d$ with respect to the inner product where $Δ…
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…
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…