Best polynomial approximation on the unit ball

摘要

Let E_n( f )_μ be the error of best approximation by polynomials of degree at most n in the space L~2(ω_μ,B~d ), where B~d is the unit ball in R~d and ω_μ(x) = (1 -||x||~2)~μ for μ > -1. Our main result shows that, for s ∈ N,where Δ and Δ_0 are the Laplace and Laplace-Beltrami operators, respectively. We also derive a bound when the right-hand side contains odd-order derivatives.