Limiting absorption principle and radiation condition for repulsive Hamiltonians
arXiv:1711.06156
Abstract
For spherically symmetric repulsive Hamiltonians we prove the Besov 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.
22 pages. arXiv admin note: substantial text overlap with arXiv:1602.07488 by other authors