5 citations · 17 across the 23 of their papers we have counts for
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Krall--type Orthogonal Polynomials in several variables
Lidia Fernandez, Teresa E. Perez, Miguel A. Pinar +1
For a bilinear form obtained by adding a Dirac mass to a positive definite moment functional in several variables, explicit formulas of orthogonal polynomials are derived from the…
Orthogonal polynomials and partial differential equations on the unit ball
Miguel Pinar, Yuan Xu
Orthogonal polynomials of degree with respect to the weight function on the unit ball in $\RR^d$ are known to satisfy the partial differential equation…
Boundedness of projection operators and Cesàro means in weighted space on the unit sphere
Feng Dai, Yuan Xu
For the weight function $\prod_{i=1}^{d+1}|x_i|^{2\k_i}$ on the unit sphere, sharp local estimates of the orthogonal projection operators are obtained and used to prove the converg…
Cesàro means of orthogonal expansions in several variables
Feng Dai, Yuan Xu
Cesàro means are studied for orthogonal expansions with respect to the weight function $\prod_{i=1}^{d}|x_i|^{2\k_i}$ on the unit sphere, and for the corresponding weight f…
Decomposition of spaces of distributions induced by Hermite expansions
Pencho Petrushev, Yuan Xu
Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on $…
Maximal function and Multiplier Theorem for Weighted Space on the Unit Sphere
Feng Dai, Yuan Xu
For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier t…