Semi-classical dispersive estimates

Semi-classical Estimates on the Scattering Determinant

Dispersive Estimates, Strichartz Estimates and Smoothing Effects

In this short expository note, we will discuss three subjects: dispersive estimates, Strichartz estimates and smoothing effects which are of great importance in the study of dispersive equations. We will focus on the Euclidean setting and try to derive the interplay among above three objects. We will mainly focus on linear problems in various contexts. Some nonlinear application will also be me...

Remarks on Dispersive Estimates and Curvature

We investigate connections between certain dispersive estimates of a (pseudo)differential operator of real principal type and the number of nonvanishing curvatures of its characteristic manifold. More precisely, we obtain sharp thresholds for the range of Lebesgue exponents depending on the specific geometry.

Dispersive Estimates for Principally Normal Pseudodifferential Operators

The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used to prove L Carleman inequalities, which in turn yield unique continuation results for various partial differential operators with rough potentials.

Dispersive Estimates for Schrödinger Operators: a Survey