Selfadjoint extensions of the multiplication operator in de Branges spaces as singular rank-one perturbations

We derive a description of the family of canonical selfadjoint extensions of the operator of multiplication in a de Branges space in terms of singular rank-one perturbations using distinguished elements from the set of functions associated with a de Branges space. The scale of rigged Hilbert spaces associated with this construction is also studied from the viewpoint of de Branges's theory.
Comment: 26 pages no figures. Typos corrected. Some remarks and an example added