Complétude asymptotique pour un modèle du transfert de charge
Comportamento asintotico dello spettro di operatori multi-quasi-ellittici di tipo Schrödinger
Comportement semi-classique du spectre des Hamiltoniens quantiques elliptiques
Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques
Confining quantum particles with a purely magnetic field
We consider a Schrödinger operator with a magnetic field (and no electric field) on a domain in the Euclidean space with a compact boundary. We give sufficient conditions on the behaviour of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of view, it means that the quantum particle is confined in the domain by the magnetic field. We construct examples in the case where the boundary is smooth as well as for polytopes; These...
Continuum spectrum for the linearized extremal eigenvalue problem with boundary reactions
We study the semilinear problem with the boundary reaction where , , is a smooth bounded domain, is a smooth, strictly positive, convex, increasing function which is superlinear at , and is a parameter. It is known that there exists an extremal parameter such that a classical minimal solution exists for , and there is no solution for . Moreover, there is a unique weak solution corresponding to the parameter . In this paper, we continue to study the spectral properties of and show...
Control theory and high energy eigenfunctions
Convexity of the first eigenfunction of the drifting Laplacian operator and its applications.
Coverings, heat kernels and spanning trees.
Das Ausstrahlungsproblem für elliptische Differentialgleichungen in Gebieten mit unbeschränkten Rand.
Dependence of a differential equation on the first eigenvalue of a suitable problem
Développement asymptotique de la densité d'états pour l'opérateur de Schrödinger aléatoire avec champ magnétique
Développements asymptotiques et effet tunnel dans l'approximation de Born-Oppenheimer
Die absolute Stetigkeit des positiven Spektrums der Schwingungsgleichungen mit oszillierendem Hauptteil.
Dirac Operations with Strongly Singular Potentials. Distinguished Self-Adjoint Extensions Constructed with a Spectral Gap Theorem and Cut-Off-Potentials.
Distribution des résonances pour le système de l'élasticité
Domain perturbations, capacity and shift of eigenvalues
After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator . If is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in Capacity in abstract Hilbert spaces and applications to higher order differential operators (Comm. P. D. E., 24:759–775,...
Eigenfunctions and fundamental solutions of the fractional two-parameter Laplacian.
Eigenfunctions of the laplacian, quantum chaos, and computation
Eigenvalue distribution for non-self-adjoint operators on compact manifolds with small multiplicative random perturbations
In this work we extend a previous work about the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint differential operators with small multiplicative random perturbations, by treating the case of operators on compact manifolds