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Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform

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  • Using a vanishing theorem for microlocally real analytic distributions and a theorem on flatness of a distribution vanishing on infinitely many hyperplanes we give a new proof of an injectivity theorem of Bélisle, Massé, and Ransford for the ray transform on $\R^n$. By means of an example we show that this result is sharp. An extension is given where real analyticity is replaced by quasianalyticity.
    Mathematics Subject Classification: Primary: 44A12; Secondary: 35A27.


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