Abel transforms with low regularity with applications to x-ray tomography on spherically symmetric manifolds. (8th November 2017) - de Hoop, Maarten V; Ilmavirta, Joonas
Abstract: We study ray transforms on spherically symmetric manifolds with a piecewise C 1, 1 metric. Assuming the Herglotz condition, the x-ray transform is injective on the space of L 2 functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a C 1, 1 metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.