Asymptotics of the spectrum of compact pseudodifferential operators in a Euclidean domain

The spectrum of selfadjoint compact pseudodifferential operators in a bounded Euclidean domain is studied. The symbol of the CDO is assumed to be a smooth matrix function. No assumptions concerning ellipticity or constant multiplicity of the eigenvalues of the matrix symbol are made. For such CDO the asymptotics of the positive and negative spectrum including remainder term estimates are obtained by the variational method. The case of an operator with “constant” symbol is singled out.
Bibliography: 11 titles.