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We give an explicit Singular Value Decomposition of the sub-Riemannian X-raytransform on the Heisenberg group with compact center. By studying the singularvalues, we obtain a two-radius theorem for integrals over sub-Riemanniangeodesics. We also state intertwining properties of distinguished differentialoperators. We conclude with a description of ongoing work.

Singular Value Decomposition for the X-ray Transforms on the Reduced Heisenberg Group, and a Two-Radius Theorem