Currently displaying 1 – 6 of 6

Showing per page

Order by Relevance | Title | Year of publication

Weighted Weyl estimates near an elliptic trajectory.

Thierry PaulAlejandro Uribe — 1998

Revista Matemática Iberoamericana

Let Ψj h and Ej h denote the eigenfunctions and eigenvalues of a Schrödinger-type operator Hh with discrete spectrum. Let Ψ(x,ξ) be a coherent state centered at a point (x,ξ) belonging to an elliptic periodic orbit, γ of action Sγ and Maslov index σγ. We consider weighted Weyl estimates of the following form:...

Semiclassical spectral estimates for Toeplitz operators

David BorthwickThierry PaulAlejandro Uribe — 1998

Annales de l'institut Fourier

Let X be a compact Kähler manifold with integral Kähler class and L X a holomorphic Hermitian line bundle whose curvature is the symplectic form of X . Let H C ( X , ) be a Hamiltonian, and let T k be the Toeplitz operator with multiplier H acting on the space k = H 0 ( X , L k ) . We obtain estimates on the eigenvalues and eigensections of T k as k , in terms of the classical Hamilton flow of H . We study in some detail the case when X is an integral coadjoint orbit of a Lie group.

Sur les mesures de Wigner.

Pierre-Louis LionsThierry Paul — 1993

Revista Matemática Iberoamericana

We study the properties of the Wigner transform for arbitrary functions in L or for hermitian kernels like the so-called density matrices. And we introduce some limits of these transforms for sequences of functions in L, limits that correspond to the semi-classical limit in Quantum Mechanics. The measures we obtain in this way, that we call Wigner measures, have various mathematical properties that we establish. In particular, we prove they satisfy, in linear situations (Schrödinger equations) or...

Page 1

Download Results (CSV)