Homogeneous Schrödinger operators on half-line

2009/11/30 by Laurent Bruneau, Bruneau, Laurent, Jan Dereziński +3 · 4 citations
Mathematics · #Spectral Theory in Mathematical Physics #advanced mathematical theories #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.0911.5569

Abstract

The differential expression L_m=-∂_x² +(m²-1/4)x^-2 defines a self-adjoint operator H_m on L²(0;∞) in a natural way when m² ≥ 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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• The Dirichlet-to-Neumann map on asymptotically anti-de Sitter spaces and holography
• Strichartz estimates for a Schrödinger equation on the half-line with a Neumann boundary condition
• Weber-Schafheitlin integrals with arbitrary exponent
• Heat kernel bounds for the fractional Laplacian with Hardy potential in angular momentum channels

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