Density of Schrödinger Weyl–Titchmarsh m functions on Herglotz functions

We show that the Herglotz functions that arise as Weyl–Titchmarsh m 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.