Boundary Behavior of Functions in the de Branges–Rovnyak Spaces |
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Authors: | Emmanuel Fricain Javad Mashreghi |
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Institution: | (1) Institut Camille Jordan, Université Lyon 1, CNRS UMR 5208, Université de Lyon, 43, boulevard du 11 Novembre 1918, F-69622 Villeurbanne, France;(2) Département de mathématiques et de statistique, Université Laval, Québec, QC, G1K 7P4, Canada |
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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.
Received: May 10, 2007. Revised: August 8, 2007. Accepted: August 8, 2007. |
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Keywords: | Primary: 46E15 46E22 Secondary: 30D55 47A15 30B40 |
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