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Uniqueness and support theorems for analytic double fibration transforms

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RNTW03 - New tomographic methods using particles

We revisit a classical topic in integral geometry and study integral transforms associated with a double fibration. This class includes various transforms encountered in tomography problems, such as (magnetic) geodesic X-ray transforms, generalized Radon transforms, and (Lorentzian) light ray transforms. If the underlying curve or surface family is real-analytic, we show that certain analytic singularities of a function can be determined from its transform under a Bolker condition. This leads to local and global uniqueness results and Helgason type support theorems for these transforms. This is joint work with Marco Mazzucchelli (ENS Lyon) and Leo Tzou (Amsterdam).

This talk is part of the Isaac Newton Institute Seminar Series series.

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