14 research outputs found
On the dynamics of WKB wave functions whose phase are weak KAM solutions of H-J equation
In the framework of toroidal Pseudodifferential operators on the flat torus
we begin by proving the closure under
composition for the class of Weyl operators with
simbols . Subsequently, we
consider when where and we exhibit the toroidal version of the
equation for the Wigner transform of the solution of the Schr\"odinger
equation. Moreover, we prove the convergence (in a weak sense) of the Wigner
transform of the solution of the Schr\"odinger equation to the solution of the
Liouville equation on written in the measure sense.
These results are applied to the study of some WKB type wave functions in the
Sobolev space with phase functions in the class
of Lipschitz continuous weak KAM solutions (of positive and negative type) of
the Hamilton-Jacobi equation for with , and to the study of the
backward and forward time propagation of the related Wigner measures supported
on the graph of
Skew Carleson measures in strongly pseudoconvex domains
International audienceGiven a bounded strongly pseudoconvex domain D in C n with smooth boundary, we give a characterization through products of functions in weighted Bergman spaces of (λ, Îł)-skew Carleson measures on D, with λ > 0 and Îł > 1 â 1 n+1