Schrödinger operators with a singular potential.
Soit un espace riemannien symétrique et l’espace des fonctions continues sur tendant vers 0 à l’infini. On démontre qu’un opérateur , invariant par les isométries de , engendre un semi-groupe fortement continu de contractions sur s’il est dissipatif et si son domaine contient les fonctions de classe à support compact.
We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower order terms. In this general setting we deduce inhomogeneous estimates. In case the group is nilpotent and the subelliptic operator is pure second order, we prove stronger homogeneous estimates. Furthermore, we prove Lipschitz stability of the estimates under small...