Comptes Rendus
no. 7-8
Mathematical Analysis
Closure of the set of pseudodifferential operators

Presented by: Jean-Michel Bony

Jean Nourrigat1
1 Laboratoire de mathématiques, EA4535 and FR.CNRS.3399, université de Reims, U.F.R. sciences exactes et naturelles, moulin de la Housse, BP 1039, 51687 Reims cedex 2, France
Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 355-358.

We determine the closure of the set of pseudodifferential operators of Calderón Vaillancourt type in the space of bounded linear operators in L2(Rn), and also the closure of the similar classes of C. Rondeaux in the Schatten class. We give representation-theoretic characterizations of these classes.

On détermine lʼadhérence de lʼensemble des opérateurs pseudodifférentiels appartenant à la classe de Calderón-Vaillancourt dans lʼespace des opérateurs bornés dans L2(Rn), et aussi des classes analogues de C. Rondeaux dans les classes de Schatten correspondantes. On donne une caractérisation de ces classes en termes de représentations de groupes.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2012.04.006

Jean Nourrigat 1

1 Laboratoire de mathématiques, EA4535 and FR.CNRS.3399, université de Reims, U.F.R. sciences exactes et naturelles, moulin de la Housse, BP 1039, 51687 Reims cedex 2, France 
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Jean Nourrigat. Closure of the set of pseudodifferential operators. Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 355-358. doi : 10.1016/j.crma.2012.04.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.006/

[1] L. Amour; M. Khodja; J. Nourrigat The classical limit of the time dependent Hartree–Fock equation. II. The Wick symbol of the solution | arXiv

[2] R. Beals Characterization of pseudo-differential operators and applications, Duke Math. J., Volume 44 (1977) no. 1, pp. 45-57

[3] A.-P. Calderón; R. Vaillancourt A class of bounded pseudo-differential operators, Proc. Natl. Acad. Sci. USA, Volume 69 (1972), pp. 1185-1187

[4] C. Rondeaux Classes de Schatten dʼopérateurs pseudo-différentiels, Ann. E.N.S., Volume 17 (1984) no. 1, pp. 67-81

[5] B. Simon Trace Ideals and Their Applications, Math. Surveys and Monographs, vol. 120, Amer. Math. Soc., 2005

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