2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142001The paper contains a simple proof of the Finch-Patch-Rakesh inversion formula for the spherical mean Radon transform in odd dimensions. This transform arises in thermoacoustic tomography. Applications are given to the Cauchy problem for the Euler-Poisson-Darboux equation with initial data on the cylindrical surface. The argument relies on the idea of analytic continuation and known properties of Erdelyi-Kober fractional integrals.Functional AnalysisAnalysis of PDEs44A12; 92C55; 65R32text