no. 3
A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform
[Un problème de Cauchy pour des opérateurs différentiels elliptiques invariants et continuité d’une transformée de Berezin généralisée.]
Ørsted, Bent1 ; Vargas, Jorge2
1 Ny Munkegade Department of Mathematics 8000 Aarhus C. (Danemark)
2 Universidad Nacional de Córdoba FAMAF-CIEM Ciudad Universitaria 5000 Córdoba (Argentine)
Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 693-702.

Dans cette note, nous généralisons les résultats de notre article précédent sur l’opérateur de Casimir et sur la transformée de Berezin, en prouvant la continuité (L 2 ,L 2 ) d’une transformée de Berezin généralisée associée à un problème de bifurcation pour une classe de représentations unitaires définie par des opérateurs elliptiques invariants. Nous prouvons aussi que, sous des conditions générales adéquates, cette transformée de Berezin généralisée est (L p ,L p )-continue pour 1≤p≤∞.

In this note, we generalize the results in our previous paper on the Casimir operator and Berezin transform, by showing the (L 2 ,L 2 )-continuity of a generalized Berezin transform associated with a branching problem for a class of unitary representations defined by invariant elliptic operators; we also show, that under suitable general conditions, this generalized Berezin transform is (L p ,L p )-continuous for 1≤p≤∞.

DOI : 10.5802/aif.2272
Classification : 22E46
Keywords: Discrete Series representations, branching laws, invariant elliptic operators
Mot clés : Séries discrètes, lois de bifurcation, opérateurs elliptiques invariants.

Ørsted, Bent 1 ; Vargas, Jorge 2

1 Ny Munkegade Department of Mathematics 8000 Aarhus C. (Danemark)
2 Universidad Nacional de Córdoba FAMAF-CIEM Ciudad Universitaria 5000 Córdoba (Argentine) 
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Ørsted, Bent; Vargas, Jorge. A Cauchy Problem for Elliptic Invariant Differential Operators and Continuity of a generalized Berezin transform. Annales de l'Institut Fourier, Tome 57 (2007) no. 3, pp. 693-702. doi : 10.5802/aif.2272. https://aif.centre-mersenne.org/articles/10.5802/aif.2272/

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