Constancy of spectra of equivariant (non-selfadjoint) operators over minimal dynamical systems

Dynamical systems method (DSM) for selfadjoint operators

Let A be a selfadjoint linear operator in a Hilbert space H. The DSM (dynamical systems method) for solving equation Av = f consists of solving the Cauchy problem u̇ = Φ(t, u), u(0) = u0, where Φ is a suitable operator, and proving that i) ∃u(t) ∀t > 0, ii) ∃u(∞), and iii) A(u(∞)) = f . It is proved that if equation Av = f is solvable and u solves the problem u̇ = i(A + ia)u − if, u(0) = u0, wher...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Non-selfadjoint Perturbations of Selfadjoint Operators in 2 Dimensions I

This is the first in a series of works devoted to small non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is periodic and the strength ǫ of the perturbation is ≫ h (or sometimes only ≫ h2) and bounded from above by hδ for some δ > 0. We get a complete asymptotic descri...

Spectral monodromy of non selfadjoint operators

We propose to build in this paper a combinatorial invariant, called the ”spectral monodromy” from the spectrum of a single (non-selfadjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting selfadjoint h-pseudodifferential operators, given ...

on the spectral properties of degenerate non-selfadjoint elliptic systems of differential operators