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arXiv · 0802.0679

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

Emmanuel Fricain·Javad Mashreghi
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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 $I$ 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.

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Emmanuel Fricain, Javad Mashreghi. 2008-02-05. Boundary behavior of functions in the de Branges--Rovnyak spaces. https://arxiv.org/abs/0802.0679

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