English

Rellich's theorem for spherically symmetric repulsive Hamiltonians

Functional Analysis 2017-04-10 v1 Mathematical Physics Analysis of PDEs math.MP

Abstract

For spherically symmetric repulsive Hamiltonians we prove Rellich's theorem, or identify the largest weighted space of Agmon-H\"ormander 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 translations. Our method is simple and elementary, and does not employ any advanced tools such as the operational calculus or the Fourier analysis.

Cite

@article{arxiv.1703.09457,
  title  = {Rellich's theorem for spherically symmetric repulsive Hamiltonians},
  author = {Kyohei Itakura},
  journal= {arXiv preprint arXiv:1703.09457},
  year   = {2017}
}

Comments

14 pages

R2 v1 2026-06-22T18:59:01.882Z