A semiclassical approach to geometric X-ray transforms in the presence of convexity

2020/12/28 by Vasy, András · 1 citation
#35S05 (Secondary) #53C65 (Primary) 35R30 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.14307

Abstract

In this short paper we introduce a variant of the approach to inverting the X-ray transform that originated in the author's work with Uhlmann. The new method is based on semiclassical analysis and eliminates the need for using sufficiently small domains and layer stripping for obtaining the injectivity and stability results, assuming natural geometric conditions are satisfied.

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