Density of Schrodinger Weyl-Titchmarsh m functions on Herglotz functions

作者：Hur Injo^*

来源：Journal of Differential Equations, 2016, 260(11): 8137-8159.

DOI：10.1016/j.jde.2016.02.017

• Canonical system
• Herglotz function
• Schrodinger operator
• Weyl-Titchmarsh m function

We show that the Herglotz functions that arise as Weyl-Titchmarsh m functions of one-dimensional Schrodinger 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.

• 出版日期2016-6-5