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Fractional Calderón problem with a potential

  • Ali Feizmohammadi
  • Katya Krupchyk
  • Gunther Uhlmann
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Abstract

We prove that the knowledge of local Cauchy data for a fractional Schrödinger equation on a smooth closed and connected Riemannian manifold of dimension at least two determines the manifold, its metric, and a smooth complex- valued potential, up to an isometry fixing the observation set. The observation set may be any nonempty open subset and no further geometric assumptions are required. The proof uses functional calculus identities to recover the local action of the resolvent of the Laplace-Beltrami operator.

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Cite

BibTeXRIS
BibTeX
@misc{feizmohammadi2026fractional,
  title = {{Fractional Calderón problem with a potential}},
  author = {Ali Feizmohammadi and Katya Krupchyk and Gunther Uhlmann},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06766},
  eprint = {2610.06766},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06766},
}
RIS
TY  - UNPB
TI  - Fractional Calderón problem with a potential
AU  - Ali Feizmohammadi
AU  - Katya Krupchyk
AU  - Gunther Uhlmann
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06766
UR  - https://arxiv.org/abs/2610.06766
AB  - We prove that the knowledge of local Cauchy data for a fractional Schrödinger equation on a smooth closed and connected Riemannian manifold of dimension at least two determines the manifold, its metric, and a smooth complex- valued potential, up to an isometry fixing the observation set. The observation set may be any nonempty open subset and no further geometric assumptions are required. The proof uses functional calculus identities to recover the local action of the resolvent of the Laplace-Beltrami operator.
ER  -