ASYMPTOTICS OF THE SPECTRUM OF COMPACT PSEUDODIFFERENTIAL OPERATORS IN A EUCLIDEAN DOMAIN
Aleksei Sergeevich Andreev · Mathematics of the USSR-Sbornik · 1990
The spectrum of selfadjoint compact pseudodifferential operators in a bounded Euclidean domain is studied. The symbol of the ΨDO is assumed to be a smooth matrix function. No assumptions concerning ellipticity or multiplicity of the eigenvalues of the matrix symbol are made. For such ΨDO 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.