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

Abstract

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.

26 pages no figures. Typos corrected. Some remarks and an example added

References in corpus (2)

• On dB spaces with nondensely defined multiplication operator and the existence of zero-free functions
• Singular Schroedinger operators as self-adjoint extensions of n-entire operators