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

Jan Boman

doi:10.3934/ipi.2010.4.619

Article Contents

2010, Volume 4, Issue 4: 619-630. Doi: 10.3934/ipi.2010.4.619

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

Jan Boman^1,

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

Received: March 2009

Published: November 2010

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

ray transform,
analytic wave front set.

Mathematics Subject Classification: Primary: 44A12; Secondary: 35A27.

Citation:

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References

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