Spectral properties of degenerate elliptic operators with matrix coefficients

Abstract

In the work we study some spectral properties of the non-self-adjoint operator $A$ in the space $\mathcal{H}^{l}=L_{2}(0,1)^{l}$ associated with a noncoercive sesquilinear form. We address the issues on completeness of a system of root vector-functions for operator $A$ in $\mathcal{ H}^{l}$, description of the domain of operator $A$, estimating resolvent of operator $A$ and asymptotic distribution of eigenvalues of operator $A$.