A well known result of Jaffard states that an arbitrary region on a torus controls, in the L sense, solutions of the free stationary and dynamical Schrödinger equations. In this note we show that the same result is valid in the presence of a potential, that is for Schrödinger operators, −∆ + V , V ∈ C∞.

A well known result of Jaffard states that an arbitrary region on a torus controls , in the L 2 sense, solutions of the free stationary and dynamical Schrödinger equations. In this note we show that the same result is valid in the presence of a potential, that is for Schrödinger operators, −∆ + V , V ∈ C ∞ .

Abstract. We consider half–infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that the elements of the inverse matrix, as well as the elements of the fundamental matrix, decay to zero. We provide a quantitative description of the decay of the fundamental matrix in terms of p–norms. The results add to the classical results of Jaffard an...

We pursue the study of the multiscale spaces Sν introduced by Jaffard in the context of multifractal analysis. We give the necessary and sufficient condition for Sν to be locally p-convex, and exhibit a sequence of p-norms that defines its natural topology. The strong topological dual of Sν is identified to another sequence space depending on ν, endowed with an inductive limit topology. As a pa...

Abstract I shall present some recent results obtained in collaboration with V. Banica and F. de la Hoz about the evolution of vortex filaments according to the so-called binormal law. After reviewing the results for filaments with one corner, we will look at the case of general polygons. The dynamics turn out to be quite complex. Among other things numerical evidence on the appearance of multif...