$\mathcal{MID}$ and safe quotients for GRWS
Document type :
Pré-publication ou Document de travail
Title :
$\mathcal{MID}$ and safe quotients for GRWS
Author(s) :
Benhida, Chafiq [Auteur]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Curto, Raúl E. [Auteur]
Exner, George R. [Auteur]
Université de Lille
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Curto, Raúl E. [Auteur]
Exner, George R. [Auteur]
Publication date :
2023-12-11
HAL domain(s) :
Mathématiques [math]
Mathématiques [math]/Analyse fonctionnelle [math.FA]
Mathématiques [math]/Analyse fonctionnelle [math.FA]
English abstract : [en]
Geometrically regular weighted shifts (in short, GRWS) are those with weights $\alpha (N,D)$ given by $\alpha_n (N,D) = \sqrt{\frac{p^n + N}{p^n + D}}$, where $p > 1$ and $(N,D)$ is fixed in the open unit square $ (-1, ...
Show more >Geometrically regular weighted shifts (in short, GRWS) are those with weights $\alpha (N,D)$ given by $\alpha_n (N,D) = \sqrt{\frac{p^n + N}{p^n + D}}$, where $p > 1$ and $(N,D)$ is fixed in the open unit square $ (-1, 1)\times (-1, 1)$. We study here the zone of pairs $ (M,P)$ for which the weight $\frac{\alpha (N,D) }{ \alpha (M,P) }$ gives rise to a moment infinitely divisible ($ \mathcal {MID}$) or a subnormal weighted shift, and deduce immediately the analogous results for product weights $\alpha (N,D) \alpha (M,P)$, instead of quotients. Useful tools introduced for this study are a pair of partial orders on the GRWS.Show less >
Show more >Geometrically regular weighted shifts (in short, GRWS) are those with weights $\alpha (N,D)$ given by $\alpha_n (N,D) = \sqrt{\frac{p^n + N}{p^n + D}}$, where $p > 1$ and $(N,D)$ is fixed in the open unit square $ (-1, 1)\times (-1, 1)$. We study here the zone of pairs $ (M,P)$ for which the weight $\frac{\alpha (N,D) }{ \alpha (M,P) }$ gives rise to a moment infinitely divisible ($ \mathcal {MID}$) or a subnormal weighted shift, and deduce immediately the analogous results for product weights $\alpha (N,D) \alpha (M,P)$, instead of quotients. Useful tools introduced for this study are a pair of partial orders on the GRWS.Show less >
Language :
Anglais
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