[Opérateurs bornés inférieurement sur les groupes de Lie gradués]
Dans cette note nous présentons un calcul pseudo-différentiel symbolique sur tous les groupes de Lie (nilpotents) gradués et, comme application, une version de lʼinégalité de Gårding. En découlent des bornes inférieures pour des opérateurs de Rockland positifs à coefficients variables ainsi que leur hypo-ellipticité Schwartz.
In this note we present a symbolic pseudo-differential calculus on any graded (nilpotent) Lie group and, as an application, a version of the sharp Gårding inequality. As a corollary, we obtain lower bounds for positive Rockland operators with variable coefficients as well as their Schwartz-hypoellipticity.
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@article{CRMATH_2013__351_1-2_13_0,
author = {Fischer, V\'eronique and Ruzhansky, Michael},
title = {Lower bounds for operators on graded {Lie} groups},
journal = {Comptes Rendus. Math\'ematique},
pages = {13--18},
publisher = {Elsevier},
volume = {351},
number = {1-2},
year = {2013},
doi = {10.1016/j.crma.2013.01.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2013.01.004/}
}
TY - JOUR AU - Fischer, Véronique AU - Ruzhansky, Michael TI - Lower bounds for operators on graded Lie groups JO - Comptes Rendus. Mathématique PY - 2013 SP - 13 EP - 18 VL - 351 IS - 1-2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.01.004/ DO - 10.1016/j.crma.2013.01.004 LA - en ID - CRMATH_2013__351_1-2_13_0 ER -
%0 Journal Article %A Fischer, Véronique %A Ruzhansky, Michael %T Lower bounds for operators on graded Lie groups %J Comptes Rendus. Mathématique %D 2013 %P 13-18 %V 351 %N 1-2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.01.004/ %R 10.1016/j.crma.2013.01.004 %G en %F CRMATH_2013__351_1-2_13_0
Fischer, Véronique; Ruzhansky, Michael. Lower bounds for operators on graded Lie groups. Comptes Rendus. Mathématique, Tome 351 (2013) no. 1-2, pp. 13-18. doi : 10.1016/j.crma.2013.01.004. http://www.numdam.org/articles/10.1016/j.crma.2013.01.004/
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