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

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