English

Homogeneous Schr\"odinger operators on half-line

Functional Analysis 2009-12-01 v1 Mathematical Physics math.MP

Abstract

The differential expression Lm=x2+(m21/4)x2L_m=-\partial_x^2 +(m^2-1/4)x^{-2} defines a self-adjoint operator H_m on L^2(0;\infty) in a natural way when m21m^2 \geq 1. We study the dependence of H_m on the parameter m, show that it has a unique holomorphic extension to the half-plane Re(m) > -1, and analyze spectral and scattering properties of this family of operators.

Keywords

Cite

@article{arxiv.0911.5569,
  title  = {Homogeneous Schr\"odinger operators on half-line},
  author = {Laurent Bruneau and Jan Derezinski and Vladimir Georgescu},
  journal= {arXiv preprint arXiv:0911.5569},
  year   = {2009}
}
R2 v1 2026-06-21T14:17:33.818Z