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.
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Communicated by Christian Gérard.
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Bruneau, L., Dereziński, J. & Georgescu, V. Homogeneous Schrödinger Operators on Half-Line. Ann. Henri Poincaré 12, 547–590 (2011). https://doi.org/10.1007/s00023-011-0078-3
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DOI: https://doi.org/10.1007/s00023-011-0078-3