The inverse problem for the local ray transform

2013/04/25 by Hanming Zhou, Zhou, Hanming
Mathematics · #35S05 #53C21 (Secondary) #53C65 (Primary) 35R30 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #math.AP #math.DG #msc:35R30 #msc:35S05 #msc:53C21 #msc:53C65

paper · pdf · doi:10.48550/arxiv.1304.7023

13 pages. arXiv admin note: substantial text overlap with arXiv:1210.2084 by other authors

arxiv created 2013/07/20 · arxiv updated 2013/07/23

Abstract

In this paper we consider the local X-ray transform for general flows. We extend the results on the local and global invertibility of the geodesic ray transform proved by Uhlmann and Vasy \citeUV to the X-ray transform for a general flow. The key improvement is that our argument for the ellipticity of the conjugated operator A_F (which is defined in Section 2) can be applied to flows other than the geodesic flow.

Citations

• The inverse problem for the local geodesic ray transform

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