$\mathcal{MID}$ and safe quotients for GRWS

Benhida, Chafiq; Curto, Raúl E.; Exner, George R.

Document type :

Pré-publication ou Document de travail

Title :

$\mathcal{MID}$ and safe quotients for GRWS

Author(s) :

Benhida, Chafiq [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Université de Lille
Curto, Raúl E. [Auteur]
Exner, George R. [Auteur]

Publication date :

2023-12-11

HAL domain(s) :

Mathématiques [math]
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 >

Language :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

2312.06390
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