English

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 mm 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