Annales Henri Poincaré

, Volume 12, Issue 3, pp 547–590 | Cite as

Homogeneous Schrödinger Operators on Half-Line

  • Laurent Bruneau
  • Jan Dereziński
  • Vladimir Georgescu


The differential expression \({L_m=-\partial_x^2+(m^2-1/4)x^{-2}}\) defines a self-adjoint operator H m on L 2(0, ∞) in a natural way when m 2 ≥ 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.


Compact Operator Closed Operator Wave Operator Numerical Range Homogeneous Operator 
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© Springer Basel AG 2011

Authors and Affiliations

  • Laurent Bruneau
    • 1
  • Jan Dereziński
    • 2
  • Vladimir Georgescu
    • 3
  1. 1.Department of Mathematics and UMR 8088 CNRSUniversity of Cergy-PontoiseCergy-PontoiseFrance
  2. 2.Department of Mathematical Methods in PhysicsFaculty of PhysicsUniversity of WarsawWarsawPoland
  3. 3.CNRS and University of Cergy-PontoiseCergy-PontoiseFrance

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