On the equality of de Branges–Rovnyak and Dirichlet spaces

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2025年6月29日

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Eugenio Dellepiane,
Marco M. Peloso,
Anita Tabacco

摘要

This work is devoted to the comparison of de Branges–Rovnyak spaces H(b) and harmonically weighted Dirichlet spaces $\mathcal {D}_\mu $ $D_{μ}$ . We completely characterize which H(b) spaces are also harmonically weighted Dirichlet spaces $\mathcal {D}_\mu $ $D_{μ}$ , when $\mu $ $μ$ is a finite sum of atoms. This is a generalization of a previous result by Costara–Ransford (Costara and Ransford J. Funct. Anal. 265(12), 3204–3218 2013): we make no assumptions on the Pythagorean pair (b, a), and we produce new examples.