Spectral functions of products of selfadjoint 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 ...

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

Spectral perturbation bounds for selfadjoint operators I∗

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for finite eigenvalues are obtained by using analyticity and monotonicity properties (rather than variational principles) and they are general enough to include ...

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.

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...