Rellich’s theorem for spherically symmetric repulsive Hamiltonians

Abstract

For spherically symmetric repulsive Hamiltonians we prove Rellich’s theorem, or identify the largest weighted space of Agmon–Hormander type where the generalized eigenfunctions are absent. The proof is intensively dependent on commutator arguments. Our novelty here is a use of conjugate operator associated with some radial flow, not with dilations and not with translations. Our method is simple and elementary, and does not employ any advanced tools such as the operational calculus or the Fourier analysis.