We characterize the polynomial decay of orbits of Hilbert space C 0-semigroups in resolvent
terms. We also show that results of the same type for general Banach space semigroups and …

Only in the last 15 years or so has the notion of semi-uniform stability, which lies between
exponential stability and strong stability, become part of the asymptotic theory of C 0 …

For all convex co-compact hyperbolic surfaces, we prove the existence of an essential
spectral gap, that is, a strip beyond the unitarity axis in which the Selberg zeta function has …

Motivated by potential applications to partial differential equations, we develop a theory of
fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends …

For a large class of semiclassical pseudodifferential operators, including Schrödinger
operators, P (h)=− h2Δg+ V (x), on compact Riemannian manifolds, we give logarithmic …

We present an overview of mathematical results and methods relevant for the spectral study
of semiclassical Schrödinger (or wave) operators of scattering systems, in cases where the …

We consider the damped wave equation on a manifold with imperfect geometric control. We
show the sub-exponential energy decay estimate in (Christianson, J Funct Anal 258 (3) …

For a large class of complete, non-compact Riemannian manifolds,(M, g), with boundary, we
prove high energy resolvent estimates in the case where there is one trapped hyperbolic …

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 Riemannian metrics G on ℝ d which are long range perturbations of the flat one, we
prove estimates for (− Δ G− λ− i ε)− n as λ→ 0, which are uniform with respect to ε, for all …