Completeness theorems related to BVPs satisfying the Lopatinskii condition for higher order elliptic equations

In this paper we consider a linear elliptic operator E with real constant coefficients of order 2m in two independent variables without lower order terms. For this equation, we consider linear BVPs in which the boundary operators T_1,...,T_m are of order m and satisfy the Lopatinskii-Shapiro condition with respect to E. We prove boundary completeness properties for the system {(T_1\om_k,..., T_m\om_k)}, where {\om_k} is a system of polynomial solutions of the equation Eu=0.