26 research outputs found
Sharp Bounds on the Number of Resonances for Symmertic Systems II. Non-Compactly Supported Perturbations
We extend the results in [5] to non-compactly supported perturbations
for a class of symmetric first order systems
Nodal domains in open microwave systems
Nodal domains are studied both for real and imaginary part
of the wavefunctions of an open microwave cavity and found to show the same
behavior as wavefunctions in closed billiards. In addition we investigate the
variation of the number of nodal domains and the signed area correlation by
changing the global phase according to
. This variation can be
qualitatively, and the correlation quantitatively explained in terms of the
phase rigidity characterising the openness of the billiard.Comment: 7 pages, 10 figures, submitted to PR
A global Carleman estimate in a transmission wave equation and application to a one-measurement inverse problem
We consider a transmission wave equation in two embedded domains in ,
where the speed is in the inner domain and in the outer
domain. We prove a global Carleman inequality for this problem under the
hypothesis that the inner domain is strictly convex and . As a
consequence of this inequality, uniqueness and Lip- schitz stability are
obtained for the inverse problem of retrieving a stationary potential for the
wave equation with Dirichlet data and discontinuous principal coefficient from
a single time-dependent Neumann boundary measurement
Diophantine tori and Weyl laws for non-selfadjoint operators in dimension two
We study the distribution of eigenvalues for non-selfadjoint perturbations of
selfadjoint semiclassical analytic pseudodifferential operators in dimension
two, assuming that the classical flow of the unperturbed part is completely
integrable. An asymptotic formula of Weyl type for the number of eigenvalues in
a spectral band, bounded from above and from below by levels corresponding to
Diophantine invariant Lagrangian tori, is established. The Weyl law is given in
terms of the long time averages of the leading non-selfadjoint perturbation
along the classical flow of the unperturbed part