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  • Journées équations aux dérivées partielles
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Microlocalization of resonant states and estimates of the residue of the scattering amplitude
Jean-François Bony; Laurent Michel
Journées équations aux dérivées partielles (2003), article no. 2, 12 p.
  • Abstract

We obtain some microlocal estimates of the resonant states associated to a resonance z 0 of an h-differential operator. More precisely, we show that the normalized resonant states are 𝒪(| Im z 0 |/h +h ∞ ) outside the set of trapped trajectories and are 𝒪(h ∞ ) in the incoming area of the phase space. As an application, we show that the residue of the scattering amplitude of a Schrödinger operator is small in some directions under an estimate of the norm of the spectral projector. Finally we prove such bound in some examples.

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MR   Zbl
DOI: 10.5802/jedp.616
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@incollection{JEDP_2003____A2_0,
     author = {Jean-Fran\c{c}ois Bony and Laurent Michel},
     title = {Microlocalization of resonant states and estimates of the residue of the scattering amplitude},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {2},
     pages = {1--12},
     publisher = {Universit\'e de Nantes},
     year = {2003},
     doi = {10.5802/jedp.616},
     zbl = {02079437},
     mrnumber = {2050588},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.616/}
}
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Jean-François Bony; Laurent Michel. Microlocalization of resonant states and estimates of the residue of the scattering amplitude. Journées équations aux dérivées partielles (2003), article  no. 2, 12 p. doi : 10.5802/jedp.616. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.616/
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