Über das Fehlen positiver Eigenwerte bei einer Klasse elliptischer Differential|operatoren.
Über die Selbstadjungiertheit von Schrödinger Operatoren.
Über Regularitätseigenschaften der Potenzräume eines Schrödinger-Operators mit singulärem Potential.
Über Verallgemeinerungen des Virialsatzes und Existenzfragen von Eigenwerten bei Schrödingeroperatoren
Un majorant du nombre des valeurs propres négatives correspondantes à l’opérateur de Schrödinger généralisé.
On donne une borne supérieur du nombre des valeurs propres négatives de l’opérateur de Schrödinger généralisé, cette borne est donnée en fonction d’un nombre fini de cube dyadiques minimaux.
Un théorème de prolongement pour l'opérateur « divergence »
Uncertainty principles for orthonormal bases
In this survey, we present various forms of the uncertainty principle (Hardy, Heisenberg, Benedicks...). We further give a new interpretation of the uncertainty principles as a statement about the time-frequency localization of elements of an orthonormal basis, which improves previous unpublished results of H. Shapiro.Finally, we reformulate some uncertainty principles in terms of properties of the free heat and shrödinger equations.
Une formule de traces pour l’opérateur de Schrödinger dans
Unique continuation for Schrödinger equations in dimensions three and four
Unique continuation for Schrödinger operators in dimension three or less
We show that the differential inequality has the unique continuation property relative to the Sobolev space , , , if satisfies the conditionfor all compact , where if , we replace by . This resolves a conjecture of B. Simon on unique continuation for Schrödinger operators, , in the case . The proof uses Carleman’s approach together with the following pointwise inequality valid for all and any
Unique continuation for Schrödinger operators with potential in Morrey spaces.
Let us consider in a domain Ω of Rn solutions of the differential inequality|Δu(x)| ≤ V(x)|u(x)|, x ∈ Ω,where V is a non smooth, positive potential.We are interested in global unique continuation properties. That means that u must be identically zero on Ω if it vanishes on an open subset of Ω.
Unitary Equivalence of Stark Hamiltonians.
Universal bounds for eigenvalues of Schrödinger operators on Riemannian manifolds.
Universal monotonicity of eigenvalue moments and sharp Lieb–Thirring inequalities
We show that phase space bounds on the eigenvalues of Schr¨odinger operators can be derived from universal bounds recently obtained by E. M. Harrell and the author via a monotonicity property with respect to coupling constants. In particular, we provide a new proof of sharp Lieb– Thirring inequalities.
Valeurs propres et résonances au voisinage d'un seuil
Weak Asymptotics for Schrödinger Evolution
In this short note, we apply the technique developed in [Math. Model. Nat. Phenom., 5 (2010), No. 4, 122-149] to study the long-time evolution for Schrödinger equation with slowly decaying potential.
Wegner estimates and Anderson localization for alloy-type potentials.
Weighted Dispersive Estimates for Solutions of the Schrödinger Equation
2000 Mathematics Subject Classification: 35L15, 35B40, 47F05.Introduction and statement of results. In the present paper we will be interested in studying the decay properties of the Schrödinger group.The authors have been supported by the agreement Brazil-France in Mathematics – Proc. 69.0014/01-5. The first two authors have also been partially supported by the CNPq-Brazil.
Wesentliche Selbstadjungiertheit eines Schrödinger-Operators.
Wüst's Theorem and Positively Perturbed Schrödinger Operators.