We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.
@article{bwmeta1.element.bwnjournal-article-cmv81i2p161bwm,
author = {Dominique Manchon},
title = {Front d'onde et propagation des singularit\'es pour un vecteur-distribution},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {161-191},
zbl = {0978.22009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv81i2p161bwm}
}
Manchon, Dominique. Front d'onde et propagation des singularités pour un vecteur-distribution. Colloquium Mathematicae, Tome 79 (1999) pp. 161-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv81i2p161bwm/
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