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Homogeneous Schr?dinger Operators on Half-Line |
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| Authors: | Laurent Bruneau Jan Derezi��ski Vladimir Georgescu |
| Institution: | 1. Department of Mathematics and UMR 8088 CNRS, University of Cergy-Pontoise, 95000, Cergy-Pontoise, France 2. Department of Mathematical Methods in PhysicsFaculty of Physics, University of Warsaw, Ho?a 74, 00-682, Warsaw, Poland 3. CNRS and University of Cergy-Pontoise, 95000, Cergy-Pontoise, France |
| Abstract: | The differential expression Lm=-?x2+(m2-1/4)x-2{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. |
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