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 $\{(T_1 ω_k , . . . , T_m ω_k )\}$, where $\{ω_k \}$ is a system of polynomial solutions of the equation $Eu = 0$.