Selfadjoint extensions of the multiplication operator in de Branges spaces as singular rank-one perturbations
Functional Analysis
2020-07-23 v3 Mathematical Physics
math.MP
Spectral Theory
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.
Keywords
Cite
@article{arxiv.1706.09400,
title = {Selfadjoint extensions of the multiplication operator in de Branges spaces as singular rank-one perturbations},
author = {Luis O. Silva and Julio H. Toloza},
journal= {arXiv preprint arXiv:1706.09400},
year = {2020}
}
Comments
26 pages no figures. Typos corrected. Some remarks and an example added