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We show that the Herglotz functions that arise as Weyl-Titchmarsh $m$functions of one-dimensional Schr\"odinger operators are dense in the space ofall Herglotz functions with respect to uniform convergence on compact subsetsof the upper half plane. This result is obtained as an application of deBranges theory of canonical systems.

Density of Schr\"odinger Weyl-Titchmarsh m functions on Herglotz functions