Boundary behavior of functions in the de Branges--Rovnyak spaces
Complex Variables
2008-02-06 v1 Functional Analysis
Abstract
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 of the boundary is enough to ensure the analyticity of these functions on . We use this property in a question related to Bernstein's inequality.
Keywords
Cite
@article{arxiv.0802.0679,
title = {Boundary behavior of functions in the de Branges--Rovnyak spaces},
author = {Emmanuel Fricain and Javad Mashreghi},
journal= {arXiv preprint arXiv:0802.0679},
year = {2008}
}