BONY, Jean-Francois; PETKOV, Vesselin

doi:10.4171/JST/49

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BONY, Jean-Francois
Institut de Mathématiques de Bordeaux [IMB]

PETKOV, Vesselin
Institut de Mathématiques de Bordeaux [IMB]

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Journal of Spectral Theory. 2013, vol. 3, p. 399-422

European Mathematical Society

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This paper is devoted to the study of a semiclassical "black box" operator $P$. We estimate the norm of its resolvent truncated near the trapped set by the norm of its resolvent truncated on rings far away from the origin. For $z$ in the unphysical sheet with $- h |ln h| < Im z < 0$, we prove that this estimate holds with a constant $h |Im z|^{-1} e^{C|Im z|/h}$. We also obtain analogous bounds for the resonances states of $P$. These results hold without any assumption on the trapped set neither any assumption on the multiplicity of the resonances.< Leer menos

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Semiclassical estimates of the cut-off resolvent for trapping perturbations

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