A completeness theorem on the boundary in Besov spaces

Let { ω k } {\{ωₖ\}} be a basis of polynomial solutions to the equation E ⁢ u = 0 {Eu=0} , where E is a higher-order elliptic operator with real constant coefficients and no lower-order terms, in any number of variables. The aim of the paper is to prove that the system { ( ω k , ∂ ν ⁡ ω k , … , ∂ ν m - 1 ⁡ ω k ) } {\{(ωₖ,∂νωₖ,,∂ᵐ⁻¹νωₖ)\}} is complete in the Besov space [ B p , p 1 - 1 / p ⁢ ( ∂ ⁡ Ω ) ] m {[B^{1-{1}/{p}}p,p(∂Ω)]ᵐ} ( 1 ≤ p < ∞ ) {(1≤ p<∞)} , Ω being a C ∞ {C∞} bounded domain in ℝ n {Rⁿ} such that ℝ n <