Operators in the Interior of Domain. Esoteric Theory

Abstract

This chapter is devoted to even more specialized results than the previous one. In Section 6.1 we extend some of the above results to conjoint spectral asymptotics for families of commuting operators (general or scalar). Then in Section 6.2 we consider scalar operators with periodic Hamiltonian flow of the principal symbol (or some perturbations of such operators) and under certain conditions we obtain spectral asymptotics with highly accurate remainder estimates; these asymptotics are not necessarily completely Weyl-type. In the case of the cluster character of the spectrum we get the asymptotic distribution of the eigenvalues inside the clusters.