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

In a bounded domain with smooth boundary, a matrix elliptic differential operator is considered. It is assumed that the eigenvalues of the symbol of lie on the positive semiaxis and outside the angle , .The principal term of the asymptotics of the function describing the distribution of the eigenvalues of in the angle is calculated. Under the condition that all the eigenvalues of the symbol lie outside , upper bounds are obtained for with reduced order of growth. The case of a selfadjoint operator is considered separately.