Cyclicity in de Branges-Rovnyak spaces
Type de document :
Compte-rendu et recension critique d'ouvrage
DOI :
Titre :
Cyclicity in de Branges-Rovnyak spaces
Auteur(s) :
Fricain, Emmanuel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Grivaux, Sophie [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Grivaux, Sophie [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Titre de la revue :
Moroccan Journal of Pure and Applied Analysis
Éditeur :
Sidi Mohamed Benabdallah University [Ifrane] Al Akhawyn University
Date de publication :
2023
ISSN :
2351-8227
Mot(s)-clé(s) en anglais :
30J05
30H10
46E22
Cyclicity
de Branges–Rovnyak spaces
forward shift operator
30H10
46E22
Cyclicity
de Branges–Rovnyak spaces
forward shift operator
Discipline(s) HAL :
Mathématiques [math]
Résumé en anglais : [en]
In this paper, we study the cyclicity problem with respect to the forward shift operator $S_b$ acting on the de Branges--Rovnyak space $\mathscr{H}(b)$ associated to a function $b$ in the closed unit ball of $H^\infty$ and ...
Lire la suite >In this paper, we study the cyclicity problem with respect to the forward shift operator $S_b$ acting on the de Branges--Rovnyak space $\mathscr{H}(b)$ associated to a function $b$ in the closed unit ball of $H^\infty$ and satisfying $\log(1-|b|)\in L^1(\mathbb T)$. We present a characterisation of cyclic vectors for $S_b$ when $b$ is a rational function which is not a finite Blaschke product. This characterisation can be derived from the description, given in [S. Luo, C. Gu, S. Richter, Higher order local Dirichlet integrals and de Branges--Rovnyak spaces, \emph{Adv. Math., \textbf{385} (2021), paper No. 107748, 47], of invariant subspaces of $S_b$ in this case, but we provide here an elementary proof. We also study the situation where $b$ has the form $b=(1+I)/2$, where $I$ is a non-constant inner function such that the associated model space $K_I=\mathscr{H}(I)$ has an orthonormal basis of reproducing kernels.Lire moins >
Lire la suite >In this paper, we study the cyclicity problem with respect to the forward shift operator $S_b$ acting on the de Branges--Rovnyak space $\mathscr{H}(b)$ associated to a function $b$ in the closed unit ball of $H^\infty$ and satisfying $\log(1-|b|)\in L^1(\mathbb T)$. We present a characterisation of cyclic vectors for $S_b$ when $b$ is a rational function which is not a finite Blaschke product. This characterisation can be derived from the description, given in [S. Luo, C. Gu, S. Richter, Higher order local Dirichlet integrals and de Branges--Rovnyak spaces, \emph{Adv. Math., \textbf{385} (2021), paper No. 107748, 47], of invariant subspaces of $S_b$ in this case, but we provide here an elementary proof. We also study the situation where $b$ has the form $b=(1+I)/2$, where $I$ is a non-constant inner function such that the associated model space $K_I=\mathscr{H}(I)$ has an orthonormal basis of reproducing kernels.Lire moins >
Langue :
Anglais
Vulgarisation :
Non
Collections :
Source :
Fichiers
- document
- Accès libre
- Accéder au document
- Cyclicity-hb-space-v6.pdf
- Accès libre
- Accéder au document