Limiting Absorption Principle and Radiation Condition for Repulsive Hamiltonians

Abstract

For spherically symmetric repulsive Hamiltonians we prove the limiting absorption principle bound, the radiation condition bounds and the limiting absorption principle. The Sommerfeld uniqueness result also follows as a corollary of these. In particular, the Hamiltonians considered in this paper cover the case of inverted harmonic oscillator. In the proofs of our theorems, we mainly use a commutator argument invented recently by Ito and Skibsted. This argument is simple and elementary, and dose not employ energy cut-offs or the microlocal analysis.