English

Limiting absorption principle and radiation condition for repulsive Hamiltonians

Mathematical Physics 2017-11-17 v1 Functional Analysis math.MP

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.

Keywords

Cite

@article{arxiv.1711.06156,
  title  = {Limiting absorption principle and radiation condition for repulsive Hamiltonians},
  author = {Kyohei Itakura},
  journal= {arXiv preprint arXiv:1711.06156},
  year   = {2017}
}

Comments

22 pages. arXiv admin note: substantial text overlap with arXiv:1602.07488 by other authors

R2 v1 2026-06-22T22:48:22.427Z