Boundary behavior of functions in the de Branges--Rovnyak spaces

Emmanuel Fricain (1) , Javad Mashreghi (2)

1 ICJ - Institut Camille Jordan
2 Université LAVAL, Département de Mathématiques et de Statistiques

This paper deals with the boundary behavior of functions in the de Branges--Rovnyak spaces. First, we give a criterion for the existence of radial limits for the derivatives of functions in the de Branges--Rovnyak spaces. This criterion generalizes a result of Ahern-Clark. Then we prove that the continuity of all functions in a de Branges--Rovnyak space on an open arc $I$ of the boundary is enough to ensure the analyticity of these functions on $I$. We use this property in a question related to Bernstein's inequality.

Domaines: Variables complexes [math.CV]; Analyse fonctionnelle [math.FA]

Emmanuel Fricain, Javad Mashreghi. Boundary behavior of functions in the de Branges--Rovnyak spaces. Complex Analysis and Operator Theory, 2008, 2 (1), pp.87-97. ⟨10.1007/s11785-007-0028-8⟩. ⟨hal-00239397⟩