On dB spaces with nondensely defined multiplication operator and the existence of zero-free functions
Mathematical Physics
2020-07-23 v3 math.MP
Abstract
In this work we consider de Branges spaces where the multiplication operator by the independent variable is not densely defined. First, we study the canonical selfadjoint extensions of the multiplication operator as a family of rank-one perturbations from the viewpoint of the theory of de Branges spaces. Then, on the basis of the obtained results, we provide new necessary and sufficient conditions for a real, zero-free function to lie in a de Branges space.
Keywords
Cite
@article{arxiv.1304.5277,
title = {On dB spaces with nondensely defined multiplication operator and the existence of zero-free functions},
author = {Luis O. Silva and Julio H. Toloza},
journal= {arXiv preprint arXiv:1304.5277},
year = {2020}
}
Comments
13 pages, no fugures. Theorem and remark have been added, typographical erros corrected