Andrzej Sołtysiak

We discuss de Branges–Rovnyak spaces ℋ ⁢ ( b ) {\mathcal{H}(b)} generated by nonextreme and rational functions b and local Dirichlet spaces of order m introduced in [S. Luo, C. Gu and S. Richter, Higher order local Dirichlet integrals and de Branges–Rovnyak spaces, Adv. Math. 385 2021, Paper No. 107748]. In that paper, the authors characterized nonextreme b for which the operator Y = S | ℋ ⁢ ( b ) {Y=S|_{\mathcal{H}(b)}} , the restriction of the shift operator S on H 2 {H^{2}} to ℋ ⁢