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