Spectral analysis of the Laplacian acting on discrete cusps and funnels

We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away from the possible embedded eigenvalues. The approach is based on a positive commutator technique

On the continuity of spectra for families of magnetic pseudodifferential operators

For families of magnetic pseudodifferential operators defined by symbols and magnetic fields depending continuously on a real parameter $\epsilon$, we show that the corresponding family of spectra also varies continuously with $\epsilon$.Comment: 22 page

Spectral analysis of the Laplacian acting on discrete cusps and funnels

Nous étudions le Laplacien agissant sur un cusp discret et un funnel discret. Nous ajoutons une perturbation longue-portée à la métrique. Puis, nous établissons un principe d'absorption limite en dehors des possibles valeurs propres plongées. Notre approche est basée sur une technique de commutateurs positifs.We study perturbations of the discrete Laplacian associated to discrete analogs of cusps and funnels. We perturb the metric and the potential in a long-range way. We establish a propagation estimate and a Limiting Absorption Principle away from the possible embedded eigenvalues. The approach is based on a positive commutator technique

On the ascent-descent spectrum

We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for such spectra

ON WEIGHTED AND PSEUDO-WEIGHTED SPECTRA OF BOUNDED OPERATORS

International audienceIn the present paper, we extend the mains results of Jeribi in [6] to weighted and pseudo-weighted spectra of operatorsin a non separable Hilbert space H. We investigate the characterization, the stability and some properties of these weighted and pseudo-weighted spectra

On shifting the principal eigenvalue of Dirichlet problem to infinity with non-transversal incompressible drift

We prove that it is always possible to add some divergence free drift vector field to some two dimensional spherical Dirichlet problem, such that the resulting principal eigenvalue lies above a prescribed bound. By construction those drift vector fields vanish on the boundary and their flow lines individually stay away from the boundary. The capacity of those drift vector fields to accelerate diffusivity originates from high frequency oscillation of the associated flow lines. The lower bounds for the spectrum are obtained through isoperimetric inequalities for flow invariant functions