Champs magnétiques classiques et quantiques
Comparing heat operators through local isometries or fibrations
Complete asymptotic expansions for eigenvalues of Dirichlet laplacian in thin three-dimensional rods
We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions...
Complete asymptotic expansions for eigenvalues of Dirichlet Laplacian in thin three-dimensional rods*
We consider the Dirichlet Laplacian in a thin curved three-dimensional rod. The rod is finite. Its cross-section is constant and small, and rotates along the reference curve in an arbitrary way. We find a two-parametric set of the eigenvalues of such operator and construct their complete asymptotic expansions. We show that this two-parametric set contains any prescribed number of the first eigenvalues of the considered operator. We obtain the complete asymptotic expansions for the eigenfunctions...
Complexified quantum rules
Comportement asymptotique de la fonction spectrale de l'opérateur de Laplace-Beltrami sur une variété ayant des singularités coniques
Comportement asymptotique des valeurs propres d'opérateurs elliptiques dégénérés
Comportement asymptotique des valeurs propres du laplacien sur un ouvert à bord fractal
Comportement asymptotique des valeurs propres d'une classe d'opérateurs elliptiques et dégénérés en dimension 2
Comportement asymptotique des valeurs propres d’une classe d’opérateurs elliptiques dégénérés en dimension
Comportement asymptotique des valeurs propres pour une classe d'opérateurs elliptiques dégénérés
Comportement asymptotique précisé du spectre d’opérateurs globalement elliptiques dans
Comportement semi-classique du spectre des Hamiltoniens quantiques elliptiques
Cônes symplectiques et opérateurs de Toeplitz
Construction of the wave group for higher order elliptic boundary value problems
Continuous spectrum of a fourth order nonhomogeneous elliptic equation with variable exponent.
Control of networks of Euler-Bernoulli beams
Control of networks of Euler-Bernoulli beams
We consider the exact controllability problem by boundary action of hyperbolic systems of networks of Euler-Bernoulli beams. Using the multiplier method and Ingham's inequality, we give sufficient conditions insuring the exact controllability for all time. These conditions are related to the spectral behaviour of the associated operator and are sufficiently concrete in order to be able to check them on particular networks as illustrated on simple examples.
Cramér's formula for Heisenberg manifolds
Let be the error term in Weyl’s law for a 3-dimensional Riemannian Heisenberg manifold. We prove that , where is a specific nonzero constant and is an arbitrary small positive number. This is consistent with the conjecture of Petridis and Toth stating that .The idea of the proof is to use the Poisson summation formula to write the error term in a form which can be estimated by the method of the stationary phase. The similar result will be also proven in the -dimensional case.