no. 4
Norm estimates for unitarizable highest weight modules
Annales de l'Institut Fourier, Tome 49 (1999) no. 4, pp. 1241-1264.

Nous considérons des familles de modules de poids dominant unitarisables (ℋ λ ) λ∈L sur une demi-droite L. Ces modules peuvent être réalisés comme des fonctions holomorphes à valeurs vectorielles sur un domaine borné symétrique 𝒟. Les fonctions polynomiales constituent un sous-ensemble dense de chaque ℋ λ , λ∈L. Dans ce travail nous comparons les normes d’un polynôme fixé dans deux espaces de Hilbert correspondant à deux paramètres différents. Comme application nous montrons que, pour tout λ∈L, le module de vecteurs hyperfonctions ℋ λ -∞ peut être réalisé comme l’espace des fonctions holomorphes sur 𝒟.

We consider families of unitarizable highest weight modules (ℋ λ ) λ∈L on a halfline L. All these modules can be realized as vector valued holomorphic functions on a bounded symmetric domain 𝒟, and the polynomial functions form a dense subset of each module ℋ λ , λ∈L. In this paper we compare the norm of a fixed polynomial in two Hilbert spaces corresponding to two different parameters. As an application we obtain that for all λ∈L the module of hyperfunction vectors ℋ λ -∞ can be realized as the space of all holomorphic functions on 𝒟.

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     author = {Kr\"otz, Bernhard},
     title = {Norm estimates for unitarizable highest weight modules},
     journal = {Annales de l'Institut Fourier},
     pages = {1241--1264},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {49},
     number = {4},
     year = {1999},
     doi = {10.5802/aif.1716},
     zbl = {0930.22013},
     mrnumber = {2001i:22013},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1716/}
}
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Krötz, Bernhard. Norm estimates for unitarizable highest weight modules. Annales de l'Institut Fourier, Tome 49 (1999) no. 4, pp. 1241-1264. doi : 10.5802/aif.1716. https://aif.centre-mersenne.org/articles/10.5802/aif.1716/

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