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Annales Henri Poincaré

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

Homogeneous Schrödinger Operators on Half-Line

  • Laurent Bruneau
  • Jan Dereziński
  • Vladimir Georgescu
Article

Abstract

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.

Keywords

Compact Operator Closed Operator Wave Operator Numerical Range Homogeneous Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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