The limiting absorption principle asserts that if H is a suitable Schrödinger operator, and f
lives in a suitable weighted L 2 space (namely H^ 0, 1/2+ σ H 0, 1/2+ σ for some σ> 0 σ> 0) …

It is well‐known that when the geometry and/or coefficients allow stable trapped rays, the
outgoing solution operator of the Helmholtz equation grows exponentially through a …

This paper is concerned with resolvent estimates on the real axis for the Helmholtz equation
posed in the exterior of a bounded obstacle with Dirichlet boundary conditions when the …

By assuming a certain localized energy estimate, we prove the existence portion of the
Strauss conjecture on asymptotically flat manifolds, possibly exterior to a compact domain …

In this paper, we show how to obtain decay estimates for the damped wave equation on a
compact manifold without geometric control via knowledge of the dynamics near the …

For a large class of semiclassical operators $ P (h)-z $ which includes Schrödinger
operators on manifolds with boundary, we construct the Quantum Monodromy operator $ M …

Localized energy estimates have become a fundamental tool when studying wave
equations in the presence of asymptotically at background geometry. Trapped rays …

In this paper we study the following phenomenon: losses in high energy, ie semiclassical,
resolvent estimates caused by trapping are removed if one truncates the resolvent …

We consider a family of rotationally symmetric, asymptotically Euclidean manifolds with two
trapped sets, one of which is unstable and one of which is semistable. We prove a sharp …

We prove global Strichartz inequalities for the Schr\" odinger equation on a large class of
asymptotically conical manifolds. Letting $ P $ be the nonnegative Laplace operator and …