PreprintCC BY 4.0arXiv
The Calderón problem for the fractional Schrödinger equation at a single point
Abstract
We revisit the Calderón problem for the fractional Schrödinger equation and prove that the potential is determined by Dirichlet-to-Neumann maps at a single exterior point, with exterior inputs varying in a disjoint open set. This holds for continuous potentials for all 0<s<1 and for bounded potentials when s≥ 1/4. For ordered nonnegative bounded potentials, one fixed nonzero nonnegative input and one point measurement suffice for every 0<s<1.
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BibTeX
@misc{harrach2026calderón,
title = {{The Calderón problem for the fractional Schrödinger equation at a single point}},
author = {Bastian Harrach and Yi-Hsuan Lin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36253},
eprint = {2610.36253},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36253},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Calderón problem for the fractional Schrödinger equation at a single point
AU - Bastian Harrach
AU - Yi-Hsuan Lin
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36253
UR - https://arxiv.org/abs/2610.36253
AB - We revisit the Calderón problem for the fractional Schrödinger equation and prove that the potential is determined by Dirichlet-to-Neumann maps at a single exterior point, with exterior inputs varying in a disjoint open set. This holds for continuous potentials for all 0<s<1 and for bounded potentials when s≥ 1/4. For ordered nonnegative bounded potentials, one fixed nonzero nonnegative input and one point measurement suffice for every 0<s<1.
ER -