- theory for a class of singular elliptic differential operators, II
-perturbations of leading coefficients of elliptic operators: Asymptotics of eigenvalues.
L'asymptotique de Weyl pour les bouteilles magnétiques
Les singularités des fonctions spectrales sur une variété riemannienne infiniment aplatie
Local invariants of spectral asymmetry.
Local Time-Decay of High Energy Scattering States for the Schrödinger Equation.
Local uniform convergence of the Riesz means of Laplace and Dirac expansions
Location of resonances generated by degenerate potential barrier.
Lower bounds for pseudo-differential operators
Magnetic barriers of compact support and eigenvalues in spectral gaps.
Mathematical analysis of electromagnetic open Waveguides
Maximally degenerate laplacians
The Laplacian of a compact Riemannian manifold is called maximally degenerate if its eigenvalue multiplicity function is of maximal growth among metrics of the same dimension and volume. Canonical spheres and CROSSes are MD, and one asks if they are the only examples. We show that a MD metric must be at least a Zoll metric with just one distinct eigenvalue in each cluster, and hence with all band invariants equal to zero. The principal band invariant is then calculated in terms of geodesic...
Measure-geometric Laplacians for partially atomic measures
Motivated by the fundamental theorem of calculus, and based on the works of W. Feller as well as M. Kac and M. G. Kreĭn, given an atomless Borel probability measure supported on a compact subset of U. Freiberg and M. Zähle introduced a measure-geometric approach to define a first order differential operator and a second order differential operator , with respect to . We generalize this approach to measures of the form , where is non-atomic and is finitely supported. We determine analytic...
Meilleures estimations asymptotiques des restes de la fonction spectrale et des valeurs propres relatifs au laplacien
Meillieurs estimations asymptotiques des restes de la fonctionn spectrale et des valeurs propres relatifs au laplacien.
Minorations de sommes de valeurs propres d'un domaine et conjecture de Polya
Non weylian spectral asymptotics with accurate remainder estimate
Nonlocal boundary value problem for second order abstract elliptic differential equation.
Normal form of the wave group and inverse spectral theory
This talk will describe some results on the inverse spectral problem on a compact riemannian manifold (possibly with boundary) which are based on V. Guillemin's strategy of normal forms. It consists of three steps : first, put the wave group into a normal form around each closed geodesic. Second, determine the normal form from the spectrum of the laplacian. Third, determine the metric from the normal form. We will try to explain all three steps and to illustrate with simple examples such as surfaces...
Nouvelle interprétation de la formule des traces de Selberg