On the Abel Basis Property of the System of Root Vector-Functions of Degenerate Elliptic Differential Operators with Singular Matrix Coefficients

We establish completeness and summability in the Abel-Lidskii sense for the system of root vector-functions of nonselfadjoint elliptic matrix operators A generated by noncoercive forms with the Dirichlet-type boundary conditions. An operator A + βE is positive for a sufficiently large β > 0 but not strongly positive in general. We obtain estimates for the eigenvalues and resolvent of A. Also, we study the resolvent of the extension $A$ of A to the corresponding negative space.