Density of Schr\"odinger Weyl-Titchmarsh m functions on Herglotz functions
Spectral Theory
2016-02-23 v3
Abstract
We show that the Herglotz functions that arise as Weyl-Titchmarsh functions of one-dimensional Schr\"odinger operators are dense in the space of all Herglotz functions with respect to uniform convergence on compact subsets of the upper half plane. This result is obtained as an application of de Branges theory of canonical systems.
Keywords
Cite
@article{arxiv.1501.01268,
title = {Density of Schr\"odinger Weyl-Titchmarsh m functions on Herglotz functions},
author = {Injo Hur},
journal= {arXiv preprint arXiv:1501.01268},
year = {2016}
}
Comments
29 pages, revised version (after changing minor errors and adding some paragraphs) to appear in Journal of Differential Equations