Inversion formulae for the spherical mean in odd dimensions and the Euler-Poisson-Darboux equation
Document Type
Article
Publication Date
4-1-2008
Abstract
The paper contains a simple proof of the Finch-Patch-Rakesh inversion formula for the spherical mean Radon transform in odd dimensions. Inversion of that transform is important for thermoacoustic tomography and represents a challenging mathematical problem. The argument relies on the idea of analytic continuation and known properties of the Erdélyi-Kober fractional integrals. The result is applied to the solution of the Cauchy problem for the Euler-Poisson-Darboux equation with initial data on the cylindrical surface. © 2008 IOP Publishing Ltd.
Publication Source (Journal or Book title)
Inverse Problems
Recommended Citation
Rubin, B. (2008). Inversion formulae for the spherical mean in odd dimensions and the Euler-Poisson-Darboux equation. Inverse Problems, 24 (2) https://doi.org/10.1088/0266-5611/24/2/025021