In this paper we develop a general, systematic, microlocal framework for the Fredholm
analysis of non-elliptic problems, including high energy (or semiclassical) estimates, which …

A hyperbolic surface is a surface with geometry modeled on the hyperbolic plane. Spectral
theory in this context refers generally to the Laplacian operator induced by the hyperbolic …

Mathematical study of scattering resonances | Bulletin of Mathematical Sciences Skip to main
content SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Bulletin …

We obtain an essential spectral gap for n-dimensional convex co-compact hyperbolic
manifolds with the dimension δ δ of the limit set close to n-1\over 2 n-1 2. The size of the gap …

We show the small data solvability of suitable semilinear wave and Klein–Gordon equations
on geometric classes of spaces, which include so-called asymptotically de Sitter and Kerr …

Fractal uncertainty principle states that no function can be localized in both position and
frequency near a fractal set. This article provides a review of recent developments on the …

We revisit Vasy's method ([27] and [28]) for showing meromorphy of the resolvent for (even)
asymptotically hyperbolic manifolds. It provides an e ffective de finition of resonances in that …

We prove a fractal uncertainty principle with exponent $\frac {d}{2}-\delta+\varepsilon $,
$\varepsilon> 0$, for Ahlfors--David regular subsets of $\mathbb R^ d $ with dimension …

In this paper we analyze the Feynman wave equation on Lorentzian scattering spaces. We
prove that the Feynman propagator exists as a map between certain Banach spaces defined …

For asymptotically hyperbolic manifolds with hyperbolic trapped sets we prove a fractal
upper bound on the number of resonances near the essential spectrum, with power …