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

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