SPECTRAL ASYMPTOTICS OF NONSELFADJOINT ELLIPTIC-SYSTEMS OF DIFFERENTIAL-OPERATORS IN BOUNDED DOMAINS

In a bounded domain OMEGA subset-of R(n) with smooth boundary, a matrix elliptic differential operator A is considered. It is assumed that the eigenvalues of the symbol of A lie on the positive semiaxis R+ and outside the angle-PHI = {z: \arg z\ less-than-or-equal-to phi}, phi is-an-element-of (0, pi). The principal term of the asymptotics of the function N(PHI)(t) describing the distribution of the eigenvalues of A in the angle-PHI is calculated. Under the condition that all the eigenvalues of the symbol lie outside PHI , upper bounds are obtained for N(PHI)(t) with reduced order of growth. The case of a selfadjoint operator A is considered separately.