Let {ω_k} be a basis of polynomial solutions to the equation 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, . . . , ∂^{m−1}_ν ω_k)} is complete in the Besov space [B^{1-1/p}_{p,p}(∂Ω)]^m (1 ≤p < ∞), Ω being a C^∞ bounded domain in R^n such that R^n \Ω is connected.
A completeness theorem on the boundary in Besov spaces
cialdea, alberto;
2026-01-01
Abstract
Let {ω_k} be a basis of polynomial solutions to the equation 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, . . . , ∂^{m−1}_ν ω_k)} is complete in the Besov space [B^{1-1/p}_{p,p}(∂Ω)]^m (1 ≤p < ∞), Ω being a C^∞ bounded domain in R^n such that R^n \Ω is connected.File in questo prodotto:
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