Propagation through trapped sets and semiclassical resolvent estimates

Kiril Datchev[1]; András Vasy[2]

  • [1] Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4397, U.S.A.
  • [2] Department of Mathematics, Stanford University, Stanford, CA 94305-2125, U.S.A.

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 6, page 2347-2377
  • ISSN: 0373-0956

Abstract

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Motivated by the study of resolvent estimates in the presence of trapping, we prove a semiclassical propagation theorem in a neighborhood of a compact invariant subset of the bicharacteristic flow which is isolated in a suitable sense. Examples include a global trapped set and a single isolated periodic trajectory. This is applied to obtain microlocal resolvent estimates with no loss compared to the nontrapping setting.

How to cite

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Datchev, Kiril, and Vasy, András. "Propagation through trapped sets and semiclassical resolvent estimates." Annales de l’institut Fourier 62.6 (2012): 2347-2377. <http://eudml.org/doc/251124>.

@article{Datchev2012,
abstract = {Motivated by the study of resolvent estimates in the presence of trapping, we prove a semiclassical propagation theorem in a neighborhood of a compact invariant subset of the bicharacteristic flow which is isolated in a suitable sense. Examples include a global trapped set and a single isolated periodic trajectory. This is applied to obtain microlocal resolvent estimates with no loss compared to the nontrapping setting.},
affiliation = {Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4397, U.S.A.; Department of Mathematics, Stanford University, Stanford, CA 94305-2125, U.S.A.},
author = {Datchev, Kiril, Vasy, András},
journal = {Annales de l’institut Fourier},
keywords = {Resolvent estimates; trapping; propagation of singularities; resolvent estimates},
language = {eng},
number = {6},
pages = {2347-2377},
publisher = {Association des Annales de l’institut Fourier},
title = {Propagation through trapped sets and semiclassical resolvent estimates},
url = {http://eudml.org/doc/251124},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Datchev, Kiril
AU - Vasy, András
TI - Propagation through trapped sets and semiclassical resolvent estimates
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 6
SP - 2347
EP - 2377
AB - Motivated by the study of resolvent estimates in the presence of trapping, we prove a semiclassical propagation theorem in a neighborhood of a compact invariant subset of the bicharacteristic flow which is isolated in a suitable sense. Examples include a global trapped set and a single isolated periodic trajectory. This is applied to obtain microlocal resolvent estimates with no loss compared to the nontrapping setting.
LA - eng
KW - Resolvent estimates; trapping; propagation of singularities; resolvent estimates
UR - http://eudml.org/doc/251124
ER -

References

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