De Branges–Rovnyak spaces and Dirichlet spaces

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• 作者：Nicolas Chevrot ; Dominique Guillot ; Thomas Ransford
• 关键词：Hilbert space ; de Branges– ; Rovnyak space ; Dirichlet space
• 刊名：Journal of Functional Analysis
• 出版年：2010
• 出版时间：1 November 2010
• 年：2010
• 卷：259
• 期：9
• 页码：2366-2383
• 全文大小：183 K

文摘

Sarason has shown that the local Dirichlet spaces may be considered as manifestations of de Branges–Rovnyak spaces , and has used this identification to give a new proof that the spaces are star-shaped. We investigate which other Dirichlet spaces arise as de Branges–Rovnyak spaces, and which other de Branges–Rovnyak spaces are star-shaped. We also prove a transfer principle which represents -spaces inside .