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Publication Date:
October 2010
ISSN:
1569-3945
DOI:
10.1515/jiip.2010.017

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Editor-in-Chief: Kabanikhin, Sergey I.

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On the inversion formulas of Pestov and Uhlmann for the geodesic ray transform

Venkateswaran P. Krishnan1

1E-mail: venkyp.krishnan@gmail.com

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 18, Issue 4, Pages 401–408, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2010.017, October 2010

Publication History:
Received:
2009-08-30
Published Online:
2010-10-20

Abstract

We generalize the inversion formulas obtained by Pestov–Uhlmann for the geodesic ray transform of functions and vector fields on 2-dimensional manifolds with boundary of constant curvature. Our formulas hold for simple 2-dimensional manifolds whose curvatures are close to a constant.

Keywords.: Inversion formulas; geodesic ray transform

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