We consider families of unitarizable highest weight modules on a halfline . All these modules can be realized as vector valued holomorphic functions on a bounded symmetric domain , and the polynomial functions form a dense subset of each module , . 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 the module of hyperfunction vectors can be realized as the space of all holomorphic functions on .
Nous considérons des familles de modules de poids dominant unitarisables sur une demi-droite . Ces modules peuvent être réalisés comme des fonctions holomorphes à valeurs vectorielles sur un domaine borné symétrique . Les fonctions polynomiales constituent un sous-ensemble dense de chaque , . 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 , le module de vecteurs hyperfonctions peut être réalisé comme l’espace des fonctions holomorphes sur .
@article{AIF_1999__49_4_1241_0, 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/} }
TY - JOUR AU - Krötz, Bernhard TI - Norm estimates for unitarizable highest weight modules JO - Annales de l'Institut Fourier PY - 1999 SP - 1241 EP - 1264 VL - 49 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1716/ DO - 10.5802/aif.1716 LA - en ID - AIF_1999__49_4_1241_0 ER -
%0 Journal Article %A Krötz, Bernhard %T Norm estimates for unitarizable highest weight modules %J Annales de l'Institut Fourier %D 1999 %P 1241-1264 %V 49 %N 4 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1716/ %R 10.5802/aif.1716 %G en %F AIF_1999__49_4_1241_0
Krötz, Bernhard. Norm estimates for unitarizable highest weight modules. Annales de l'Institut Fourier, Volume 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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