Geometrically regular weighted shifts

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

Type de document :

Pré-publication ou Document de travail

URL permanente :

http://hdl.handle.net/20.500.12210/121620

Titre :

Geometrically regular weighted shifts

Auteur(s) :

Benhida, Chafiq [Auteur]

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

Date de publication :

2023-09-11

Discipline(s) HAL :

Mathématiques [math]
Mathématiques [math]/Analyse fonctionnelle [math.FA]

Résumé en anglais : [en]

We study a general class of weighted shifts whose weights $\alpha$ are given by $\alpha_n = \sqrt{\frac{p^n + N}{p^n + D}}$, where $p > 1$ and $N$ and $D$ are parameters so that $(N,D) \in (-1, 1)\times (-1, 1)$. Some few ...
Lire la suite >We study a general class of weighted shifts whose weights $\alpha$ are given by $\alpha_n = \sqrt{\frac{p^n + N}{p^n + D}}$, where $p > 1$ and $N$ and $D$ are parameters so that $(N,D) \in (-1, 1)\times (-1, 1)$. Some few examples of these shifts have appeared previously, usually as examples in connection with some property related to subnormality. In sectors nicely arranged in the unit square in $(N,D)$, we prove that these geometrically regular weighted shifts exhibit a wide variety of properties: moment infinitely divisible, subnormal, $k$- but not $(k+1)$-hyponormal, or completely hyperexpansive, and with a variety of well-known functions (such as Bernstein functions) interpolating their weights squared or their moment sequences. They provide subshifts of the Bergman shift with geometric, not linear, spacing in the weights which are moment infinitely divisible. This new family of weighted shifts provides a useful addition to the library of shifts with which to explore new definitions and properties.Lire moins >

Langue :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T14:13:33Z

Fichiers

2309.05888
Accès libre
Accéder au document

Geometrically regular weighted shifts BibTeX CSV Excel RIS

Fichiers

Geometrically regular weighted shifts

BibTeX

CSV

Excel

RIS