# American Institute of Mathematical Sciences

November  2010, 4(4): 619-630. doi: 10.3934/ipi.2010.4.619

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

 1 Department of Mathematics, Stockholm University, SE-10691 Stockholm

Received  March 2009 Published  September 2010

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.
Citation: Jan Boman. Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform. Inverse Problems & Imaging, 2010, 4 (4) : 619-630. doi: 10.3934/ipi.2010.4.619
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