# 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

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topDatchev, 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 -

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