A local uniqueness theorem for  weighted Radon transforms

Jan Boman

doi:10.3934/ipi.2010.4.631

Article Contents

2010, Volume 4, Issue 4: 631-637. Doi: 10.3934/ipi.2010.4.631

This issue Previous Article Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform Next Article Special functions

A local uniqueness theorem for weighted Radon transforms

Jan Boman^1,

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

Received: July 2009

Revised: November 2009

Published: November 2010

Abstract / Introduction Related Papers Cited by

Abstract

We consider a weighted Radon transform in the plane, $R_m(\xi, \eta) = \int_{\R} f(x, \xi x + \eta) m(x,\xi,\eta) dx$, where $m(x,\xi,\eta)$ is a smooth, positive function. Using an extension of an argument of Strichartz we prove a local injectivity theorem for $R_m$ for essentially the same class of $m(x,\xi,\eta)$ that was considered by Gindikin in his article in this issue.

Keywords:

Radon transform,
weighted Radon transform.

Mathematics Subject Classification: 44A12.

Citation:

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References

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