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arXiv · 2610.36253

The Calderón problem for the fractional Schrödinger equation at a single point

Bastian Harrach·Yi-Hsuan Lin
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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 $s\geq 1/4$. For ordered nonnegative bounded potentials, one fixed nonzero nonnegative input and one point measurement suffice for every $0<s<1$.

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Bastian Harrach, Yi-Hsuan Lin. 2026-10-26. The Calderón problem for the fractional Schrödinger equation at a single point. https://arxiv.org/abs/2610.36253

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