ESTIMATES FOR EIGENVALUES AND COMPLETENESS OF EIGENFUNCTIONS OF NON SELFADJOINT SEMIELLIPTIC DIFLERENTIAL OPERATORS

Abstract

This paper is a continuation of [1] for a certain class of non-self-adjoint semi-elliptic operators. In Section 1, an estimate for the eigenvalues of a class of non-self-adjoint semi-elliptic operators in a bounded domain is proved. In Section 2, the completeness of the eigenfunctions in L₂(Ω) is demonstrated; more precisely, it is proved that sp’(T)= L₂(Ω), where sp’(T) denotes the closed subspace covered by the eigenvectors of T corresponding to the non-zero eigenvalues.