Title
Method of analytic continuation for the inverse spherical mean transform in constant curvature spaces
Document Type
Article
Publication Date
11-1-2012
Abstract
The following problem arises in thermoacoustic tomography and has intimate connection with PDEs and integral geometry. Reconstruct a function f supported in an n-dimensional ball B given the spherical means of f over all geodesic spheres centered on the boundary of B. We propose a new approach to this problem, which yields explicit reconstruction formulas in arbitrary constant curvature space, including euclidean space ℝn, the n-dimensional sphere, and hyperbolic space. The main idea is analytic continuation of the corresponding operator families. The results are applied to inverse problems for a large class of Euler-Poisson-Darboux equations in constant curvature spaces of arbitrary dimension. © 2012 Hebrew University Magnes Press.
Publication Source (Journal or Book title)
Journal d'Analyse Mathematique
First Page
623
Last Page
656
Recommended Citation
Antipov, Y., Estrada, R., & Rubin, B. (2012). Method of analytic continuation for the inverse spherical mean transform in constant curvature spaces. Journal d'Analyse Mathematique, 118 (2), 623-656. https://doi.org/10.1007/s11854-012-0046-y