Title :

CYCLICITY OF THE SHIFT OPERATOR AND A RELATED COMPLETENESS PROBLEM IN DE BRANGES-ROVNYAK SPACES

Author(s) :

Fricain, Emmanuel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Lebreton, Romain [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

English keyword(s) :

Cyclicity
De branges-Rovnyak spaces
Shift operator
Cauchy transform

HAL domain(s) :

Mathématiques [math]/Variables complexes [math.CV]
Mathématiques [math]/Analyse fonctionnelle [math.FA]

English abstract : [en]

In this paper, we study the cyclic vectors of the shift operator $S_b$ acting on de Branges--Rovnyak space $\mathcal H(b)$ associated to a non-extreme point of the closed unit ball of $H^\infty$. We highlight an interesting ...
Show more >In this paper, we study the cyclic vectors of the shift operator $S_b$ acting on de Branges--Rovnyak space $\mathcal H(b)$ associated to a non-extreme point of the closed unit ball of $H^\infty$. We highlight an interesting link with a completeness problem that we study using the Cauchy transform. This enables us to obtain some nice consequences on cyclicity.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL