PreprintCC BY 4.0arXiv
Unique continuation at infinity for potentials with arbitrary radial growth
Abstract
Let G be any given continuous positive function on ℝ+. Let V be radial with |V(x)|≤ G(|x|). We prove a Landis-type theorem for any real-valued solution of Δu=Vu on ℝn. We construct a decay threshold e−g(r), where g is a strictly increasing function which can be computed explicitly in terms of G. Under suitable assumptions the exponent in the decay threshold is proportional to the Agmon distance associated with G.
Related
- Unique continuation at infinity for Schrödinger equations with Reverse Hölder Potentials
- Quantitative Unique Continuation on Simplex and ℤn
- Strong Unique Continuation for Fractional Schrödinger Operators
- Radial Convergence along Decreasing Coordinate Radii in \texorpdfstring{H∞(T∞)}{H-infinity(T-infinity)}
- Discrete Unique Continuation on Simplex
BibTeX
@misc{ueberschaer2026unique,
title = {{Unique continuation at infinity for potentials with arbitrary radial growth}},
author = {Henrik Ueberschaer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.07276},
eprint = {2608.07276},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.07276},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Unique continuation at infinity for potentials with arbitrary radial growth
AU - Henrik Ueberschaer
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2608.07276
UR - https://arxiv.org/abs/2608.07276
AB - Let G be any given continuous positive function on ℝ_+. Let V be radial with |V(x)|≤ G(|x|). We prove a Landis-type theorem for any real-valued solution of Δu=Vu on ℝ^n. We construct a decay threshold e^−g(r), where g is a strictly increasing function which can be computed explicitly in terms of G. Under suitable assumptions the exponent in the decay threshold is proportional to the Agmon distance associated with G.
ER -