Resonance Free Domains for Non Globally Analytic Potentials

By André Martinez. 2002

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Fractal upper bounds on the density of semiclassical resonances (2005, result): “[20] A. Martinez, Resonance free domains for non globally analytic potentials, Ann.”
Pseudospectra of semiclassical (pseudo‐) differential operators (2004, methodology): “In a related c ontext of the absence of resonances, Martinez [21] recently used similar method s.”
Quantum decay rates in chaotic scattering (2007, background): “impler scattering situation, namely an operatorP♯= P♯(h)satisfying theassumptions of§3.2andforwhich the associatedclassical ﬂow is non-trapping at energy E, that is, KE = ∅. From a result of Martinez [26], we have χ(P♯− z)−1χ= O(1/h), z∈ D(E,Ch), see [28, Proposition 3.1]3. Below we will need an est”
Decay and Non-Decay of the Local Energy for the Wave Equation on the De Sitter–Schwarzschild Metric (2007, methodology): “A. Martinez, Resonance free domains for non globally analytic potentials, Ann.”
Quasi-Normal Modes and Exponential Energy Decay for the Kerr-de Sitter Black Hole (2010, methodology): “We then analyse the corresponding classical flow; it is either nontrapping at zero energy, in which case the usual escape function construction (as in, for example, [27]) applies (Proposition 7.”