Lower bounds for operators on graded Lie groups

Véronique Fischer; Michael Ruzhansky

doi:10.1016/j.crma.2013.01.004

Mathematical Analysis/Harmonic Analysis

Lower bounds for operators on graded Lie groups
[Opérateurs bornés inférieurement sur les groupes de Lie gradués]

Présenté par : the Editorial Board

Véronique Fischer ¹ ; Michael Ruzhansky ²

¹ Universita degli studi di Padova, DMMMSA, Via Trieste 63, 35121 Padova, Italy
² Department of Mathematics, Imperial College London, 180 Queenʼs Gate, London SW7 2AZ, United Kingdom

Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 13-18.

Résumé
Abstract

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.

Reçu le : 2012-08-02
Accepté le : 2013-01-10
Publié le : 2013-01-01

DOI : 10.1016/j.crma.2013.01.004

Affiliations des auteurs :

Véronique Fischer ¹ ; Michael Ruzhansky ²

¹ Universita degli studi di Padova, DMMMSA, Via Trieste 63, 35121 Padova, Italy
² Department of Mathematics, Imperial College London, 180 Queenʼs Gate, London SW7 2AZ, United Kingdom

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     title = {Lower bounds for operators on graded {Lie} groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {13--18},
     publisher = {Elsevier},
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     year = {2013},
     doi = {10.1016/j.crma.2013.01.004},
     language = {en},
}

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Véronique Fischer; Michael Ruzhansky. Lower bounds for operators on graded Lie groups. Comptes Rendus. Mathématique, Volume 351 (2013) no. 1-2, pp. 13-18. doi : 10.1016/j.crma.2013.01.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.01.004/

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