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Showing 2006 · math.CAShow all
3 papers · 2 filters
math.CA2006
Sobolev orthogonal polynomials defined via gradient on the unit ball
Yuan Xu
An explicit family of polynomials on the unit ball of $\RR^d$ is constructed, so that it is an orthonormal family with respect to the inner product $$ < f,g > = ρ\int_{B^d}\n…
math.CA2006
Localized polynomial frames on the ball
Pencho Petrushev, Yuan Xu
Almost exponentially localized polynomial kernels are constructed on the unit ball in $\RR^d$ with weights %functions , , by smoothing out…
math.CA2006★ 1 cited
Jacobi decomposition of weighted Triebel-Lizorkin and Besov spaces
George Kyriazis, Pencho Petrushev, Yuan Xu
The Littlewood-Paley theory is extended to weighted spaces of distributions on with Jacobi weights $ \w(t)=(1-t)^α(1+t)^β. $ Almost exponentially localized polynomial elem…