Mathematical Analysis/Harmonic Analysis
On the differentiable vectors for contragredient representations
Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 513-516.

We establish a few simple results on contragredient representations of Lie groups, with a view toward applications to the abstract characterization of some spaces of pseudo-differential operators. In particular, this method provides an abstract approach to J. Nourrigatʼs recent description of the norm closure of the pseudo-differential operators of order zero.

On obtient quelques résultats sur les représentations contragrédientes des groupes de Lie qui permettent dʼaborder, dʼune manière abstraite, la caractérisation de lʼadhérence normique de lʼensemble des opérateurs pseudodifférentiels dʼordre zero obtenue récemment par J. Nourrigat.

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Accepted:
Published online:
DOI: 10.1016/j.crma.2013.07.017
Beltita, Ingrid 1; Beltita, Daniel 1

1 Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania
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Beltita, Ingrid; Beltita, Daniel. On the differentiable vectors for contragredient representations. Comptes Rendus. Mathématique, Volume 351 (2013) no. 13-14, pp. 513-516. doi : 10.1016/j.crma.2013.07.017. http://www.numdam.org/articles/10.1016/j.crma.2013.07.017/

[1] Amrein, W.O.; Boutet de Monvel, A.; Georgescu, V. C0-groups, commutator methods and spectral theory of N-body Hamiltonians, Birkhäuser Verlag, Basel, 1996

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

[3] Beltiţă, I.; Beltiţă, D. Smooth vectors and Weyl–Pedersen calculus for representations of nilpotent Lie groups, Ann. Univ. Buchar. Math. Ser., Volume 58 (2010) no. 1, pp. 17-46

[4] Beltiţă, I.; Beltiţă, D. Boundedness for Weyl–Pedersen calculus on flat coadjoint orbits | arXiv

[5] Cordes, H.O. The Technique of Pseudodifferential Operators, Cambridge University Press, Cambridge, UK, 1995

[6] Gårding, L. Note on continuous representations of Lie groups, Proc. Natl. Acad. Sci. USA, Volume 33 (1947), pp. 331-332

[7] Melo, S.T. Smooth operators for the regular representation on homogeneous spaces, Studia Math., Volume 142 (2000) no. 2, pp. 149-157

[8] Neeb, K.-H. On differentiable vectors for representations of infinite dimensional Lie groups, J. Funct. Anal., Volume 259 (2010), pp. 2814-2855

[9] van Neerven, J. The Adjoint of a Semigroup of Linear Operators, Springer-Verlag, Berlin, 1992

[10] Nourrigat, J. Closure of the set of pseudodifferential operators, C. R. Acad. Sci. Paris, Ser. I, Volume 350 (2012) no. 7–8, pp. 355-358

[11] Poulsen, N.S. On C-vectors and intertwining bilinear forms for representations of Lie groups, J. Funct. Anal., Volume 9 (1972), pp. 87-120

[12] Taylor, M.E. Beals–Cordes-type characterizations of pseudodifferential operators, Proc. Amer. Math. Soc., Volume 125 (1997), pp. 1711-1716

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