Low energy resolvent estimates for slowly decaying attractive potentials
Mathematical Physics
2026-01-06 v1 Analysis of PDEs
math.MP
Abstract
We discuss the low energy resolvent estimates for the Schr\"odinger operator with slowly decaying attractive potential. The main results are Rellich's theorem, the limiting absorption principle and Sommerfeld's uniqueness theorem. For the proofs we employ an elementary commutator method due to Ito--Skibsted, for which neither of microlocal or functional-analytic techniques is required.
Keywords
Cite
@article{arxiv.2601.01102,
title = {Low energy resolvent estimates for slowly decaying attractive potentials},
author = {Kenichi Ito and Tomoya Tagawa},
journal= {arXiv preprint arXiv:2601.01102},
year = {2026}
}