Comptes Rendus
Complex analysis/Functional analysis
Pluriharmonic Clark measures and analogs of model spaces
[Mesures de Clark pluriharmoniques et analogues des espaces modèles]
Comptes Rendus. Mathématique, Volume 357 (2019) no. 1, pp. 7-12.

Soit Bd la boule unité de Cd, d1. Étant donnée une fonction intérieure I:BdB1, nous étudions la famille correspondante σα[I], αB1, de mesures de Clark pluriharmoniques sur la sphère complexe. Nous introduisons et étudions les opérateurs unitaires Uα entre des analogues des espaces modèles et L2(σα), αB1. En particulier, nous caractérisons explicitement l'ensemble des Uαf telles que fσα soit une mesure pluriharmonique.

Let Bd denote the unit ball of Cd, d1. Given an inner function I:BdB1, we study the corresponding family σα[I], αB1, of pluriharmonic Clark measures on the complex sphere. We introduce and investigate related unitary operators Uα mapping analogs of model spaces onto L2(σα), αB1. In particular, we explicitly characterize the set of Uαf such that fσα is a pluriharmonic measure.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.11.013

Aleksei B. Aleksandrov 1, 2 ; Evgueni Doubtsov 1

1 St. Petersburg Department of V.A. Steklov Institute of Mathematics, Fontanka 27, St. Petersburg 191023, Russia
2 Department of Mathematics and Mechanics, St. Petersburg State University, Universitetski pr. 28, St. Petersburg, 198504, Russia
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Aleksei B. Aleksandrov; Evgueni Doubtsov. Pluriharmonic Clark measures and analogs of model spaces. Comptes Rendus. Mathématique, Volume 357 (2019) no. 1, pp. 7-12. doi : 10.1016/j.crma.2018.11.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.11.013/

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This research was supported by the Russian Science Foundation (grant No. 18-11-00053).

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