De Branges–Rovnyak spaces and Dirichlet spaces

By N. Chevrot, D. Guillot, Thomas Ransford. 2010

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

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/905b25b081aa810821b4c1d3f560c1e2edc74fe3