Injectivity of the Heisenberg X-ray transform

نویسندگان

چکیده

We initiate the study of X-ray tomography on sub-Riemannian manifolds, for which Heisenberg group exhibits simplest nontrivial example. With language Fourier transform, we prove an operator-valued incarnation Slice Theorem, and apply this new tool to show that a sufficiently regular function is determined by its line integrals over geodesics. also consider family taming metrics g? approximating metric, associated transform injective all ?>0. This result gives concrete example in geometry with abundance conjugate points.

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ژورنال

عنوان ژورنال: Journal of Functional Analysis

سال: 2021

ISSN: ['0022-1236', '1096-0783']

DOI: https://doi.org/10.1016/j.jfa.2020.108886