Density of Schrödinger Weyl-Titchmarsh m functions on Herglotz functions
arXiv:1501.01268
Abstract
We show that the Herglotz functions that arise as Weyl-Titchmarsh functions of one-dimensional Schrödinger 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.
29 pages, revised version (after changing minor errors and adding some paragraphs) to appear in Journal of Differential Equations