English

The boundary control approach to the Titchmarsh-Weyl $m-$function

Analysis of PDEs 2025-05-30 v1 Spectral Theory

Abstract

We link the Boundary Control Theory and the Titchmarsh-Weyl Theory. This provides a natural interpretation of the AA-amplitude due to Simon and yields a new efficient method to evaluate the Titchmarsh-Weyl mm-function associated with the Schr\"{o}dinger operator H=x2+q(x)H=-\partial _{x}^{2}+q\left( x\right) on L2(0,)L_{2}\left( 0,\infty \right) with Dirichlet boundary condition at x=0.x=0.

Keywords

Cite

@article{arxiv.2505.23332,
  title  = {The boundary control approach to the Titchmarsh-Weyl $m-$function},
  author = {S. A. Avdonin and V. S. Mikhaylov and A. V. Rybkin},
  journal= {arXiv preprint arXiv:2505.23332},
  year   = {2025}
}
R2 v1 2026-07-01T02:48:12.689Z