Équations elliptiques fuchsiennes du second ordre et valeurs propres asymptotiques
For the Dirichlet Laplacian in the exterior of a strictly convex obstacle, we show that the number of scattering poles of modulus in a small angle near the real axis, can be estimated by Const for sufficiently large depending on . Here is the dimension.
Nous donnons le comportement asymptotique de valeurs propres d’opérateurs pseudodifférentiels autoadjoints, hypoelliptiques avec perte de dérivées dans le cas où la variété caractéristique est symplectique. Nous généralisatons ainsi la formule du relative aux opérateurs à caractéristiques doubles établie par A. Menikoff et J. Sjöstrand.
In [23] M. Pierre introduced parabolic Dirichlet spaces. Such spaces are obtained by considering certain families of Dirichlet forms. He developed a rather far-reaching and general potential theory for these spaces. In particular, he introduced associated capacities and investigated the notion of related quasi-continuous functions. However, the only examples given by M. Pierre in [23] (see also [22]) are Dirichlet forms arising from strongly parabolic differential operators of second order. To...
We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.