Spectral theory of some non-selfadjoint linear differential operators

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

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 ...

Spectral instability for non-selfadjoint operators∗

We describe a recent result of M. Hager, stating roughly that for nonselfadjoint ordinary differential operators with a small random perturbation we have a Weyl law for the distribution of eigenvalues with a probability very close to 1.

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

Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

We derive a spectral representation for the oblate spheroidal wave operator, which is holomorphic in the aspherical parameter Ω in a neighborhood of the real line. For real Ω, estimates are derived for all eigenvalue gaps uniformly in Ω. The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex Ω is deriv...