Resolvent estimates for non-selfadjoint operators with double characteristics

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

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Rational invariant tori , phase space tunneling , and spectra for non - selfadjoint operators in dimension 2

We study spectral asymptotics and resolvent bounds for non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Spectral contributions coming from rational invariant Lagrangian tori are analyzed. Estimating the tunnel effect between strongly irrational (Diophantine) and rational...

Norm estimates for resolvents of non-selfadjoint operators having Hilbert-Schmidt inverse ones

The paper is devoted to an invertible linear operator whose inverse is a Hilbert Schmidt operator and imaginary Hermitian component is bounded. Numerous regular differential and integro-differential operators satisfy these conditions. A sharp norm estimate for the resolvent of the considered operator is established. It gives us estimates for the semigroup and so-called Hirsch operator functions...

Spectral inequalities for non-selfadjoint elliptic operators and application to the null-controllability of parabolic systems

We consider elliptic operators A on a bounded domain, that are compact perturbations of a selfadjoint operator. We first recall some spectral properties of such operators: localization of the spectrum and resolvent estimates. We then derive a spectral inequality that measures the norm of finite sums of root vectors of A through an observation, with an exponential cost. Following the strategy of...