Abstract
For a positive Borel measure μ in the unit disc, we examine which weighted Dirichlet spaces Dμ can be identified with de Branges-Rovnyak spaces Hb, with equivalent norms. We prove a necessary condition for the equality Dμ=Hb and we explore its consequences. For Carleson measures μ, we give a necessary and sufficient condition for the equality Dμ=Hbμ, for a certain outer function bμ related with the balayage of μ on the unit circle, and we provide examples of those spaces.
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