A new type of solutions for a singularly perturbed elliptic Neumann problem.
Asymptotic expansion in time of the Schrödinger group on conical manifolds
For Schrödinger operator on Riemannian manifolds with conical end, we study the contribution of zero energy resonant states to the singularity of the resolvent of near zero. Long-time expansion of the Schrödinger group is obtained under a non-trapping condition at high energies.
Asymptotics for Bergman-Hodge kernels for high powers of complex line bundles
In this paper we obtain the full asymptotic expansion of the Bergman-Hodge kernel associated to a high power of a holomorphic line bundle with non-degenerate curvature. We also explore some relations with asymptotic holomorphic sections on symplectic manifolds.
Asymptotics of holomorphic sections of powers of a positive line bundle
Averaging method for differential equations perturbed by dynamical systems
In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption...
Averaging method for differential equations perturbed by dynamical systems
In this paper, we are interested in the asymptotical behavior of the error between the solution of a differential equation perturbed by a flow (or by a transformation) and the solution of the associated averaged differential equation. The main part of this redaction is devoted to the ascertainment of results of convergence in distribution analogous to those obtained in [10] and [11]. As in [11], we shall use a representation by a suspension flow over a dynamical system. Here, we make an assumption...
Conditions de Bohr-Sommerfeld pour les singularités focus-focus et monodromie quantique
Je présenterai les résultats d’une étude microlocale détaillée du spectre joint de deux opérateurs h-pseudo-différentiels qui commutent sur une variété de dimension deux en présence d’une singularité dite «focus-focus». L’étude couvre par exemple le cas du pendule sphérique étudié par Duistermaat, ou du fond de la bouteille de champagne, mais les phénomènes observés sont universels. On en observe principalement deux: une accumulation de valeurs propres au voisinage de la singularité en par rapport...
Corner Mellin operators and conormal asymptotics
Corrigendum to: Asymptotic expansion in time of the Schrödinger group on conical manifolds
We correct an error in the normalizing constant of resonant states.
Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale
On obtient ici le développement asymptotique, en temps petit et sur la diagonale, du noyau de la chaleur associé à un opérateur dégénéré du second ordre satisfaisant à la condition forte d’hypoellipticité de Hörmander.
Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus
Discrete version of Dungey’s proof for the gradient heat kernel estimate on coverings
We obtain another proof of a Gaussian upper estimate for a gradient of the heat kernel on cofinite covering graphs whose covering transformation group has a polynomial volume growth. It is proved by using the temporal regularity of the discrete heat kernel obtained by Blunck [2] and Christ [3] along with the arguments of Dungey [7] on covering manifolds.
Dispersive estimates for a linear wave equation with electromagnetic potential.
Eigenvalue asymptotics for Neumann Laplacian in domains with ultra-thin cusps
Asymptotics with sharp remainder estimates are recovered for number of eigenvalues of the generalized Maxwell problem and for related Laplacians which are similar to Neumann Laplacian. We consider domains with ultra-thin cusps (with ) width ; ) and recover eigenvalue asymptotics with sharp remainder estimates.
Equations de Fokker-Planck géométriques II : estimations hypoelliptiques maximales
Nous donnons des résultats analytiques sur les propriétés de régularité du laplacien hypoelliptique de Jean-Michel Bismut et plus généralement sur les opérateurs de type Fokker-Planck géométrique agissant sur le fibré cotangent d’une variété riemannienne compacte . En particulier, nous prouvons un résultat d’hypoellipticité maximale pour , et nous en déduisons des bornes sur la localisation de ses valeurs spectrales.
Geometric P.D.E.'s with isolated singularities.
Heat content asymptotics for operators to Laplace type with Neumann boundary conditions.
Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function
AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37We point out the importance of the integral representations of the logarithmic derivative of the Selberg zeta function valid up to the critical line, i.e. in the region that includes the right half of the critical strip, where the Euler product definition of the Selberg zeta function does not hold. Most recent applications to the behavior of the Selberg zeta functions associated to a degenerating sequence of finite volume, hyperbolic manifolds of...
Laplaciens en interaction.
Le comportement asymptotique des fonctions propres du laplacien d'après Schnirelman et Zelditch