Positivity Preserving Multiapproximation

摘要

We show that the degree of copositive multipolynomial approximation to a function f ∈ L_p[0,1]~d, 0 < p < ∞ which changes signs finitely many times in [0,1]~d, can be estimated by C(p,d,r) (1+1~d) ω_2(f,δ,[0,1]~d)_p, where δ = (1,...,1).