Semi-classical estimates for the resolvent in nontrapping geometries

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Geometric control in the presence of a black box (2004, methodology): “We can use the microlocal defect measures arguments as in [6]: we first prove (6.”
Strichartz estimates for long range perturbations (2005, methodology): “ll that such resolvent estimates were extensively studied in particular in connection with the local energy decay for the wave equation (∂2 t − ∆g)u= 0. For a proof of (6.2), we refer for instance to [27, 5]. Notice that Proposition 6.1 is the only place in the proof of Theorem 2 where we use the no”
Global Strichartz Estimates for Nontrapping Geometries: About an Article by H. Smith and C. Sogge (2002, background): “…j j >> 1 in greater generalities by Lax and Phillips (1989), Melrose and Sj€ostrand (1978, 1982)), Tang and Zworski (2000), Vainberg (1968) (see also Burq (2002) for a self contained proof which joined with the results in Burq (1997) would relax the smoothness assumption required in these articles…”