This work is devoted to the comparison of de Branges–Rovnyak H(b) spaces harmonically weighted Dirichlet spaces Dμ. We completely char- acterize which H(b) spaces are also harmonically weighted Dirichlet spaces Dμ, when μ is a finite sum of atoms. This is a generalization of a previous result by Costara–Ransford [8]: we make no assumptions on the Pythagorean pair (b, a), and we produce new examples.
On the equality of de Branges–Rovnyak and Dirichlet spaces / E. Dellepiane, M.M. Peloso, A. Tabacco. - In: COMPLEX ANALYSIS AND OPERATOR THEORY. - ISSN 1661-8254. - 19:5(2025), pp. 119.1-119.16. [10.1007/s11785-025-01747-x]
On the equality of de Branges–Rovnyak and Dirichlet spaces
M.M. PelosoSecondo
;
2025
Abstract
This work is devoted to the comparison of de Branges–Rovnyak H(b) spaces harmonically weighted Dirichlet spaces Dμ. We completely char- acterize which H(b) spaces are also harmonically weighted Dirichlet spaces Dμ, when μ is a finite sum of atoms. This is a generalization of a previous result by Costara–Ransford [8]: we make no assumptions on the Pythagorean pair (b, a), and we produce new examples.
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