Spherical Means in Odd Dimensions and EPD equations

2007/11/13 by Boris Rubin, Rubin, Boris
Mathematics · #44A12 #65R32 #92C55 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA #msc:44A12 #msc:65R32 #msc:92C55

paper · pdf · doi:10.48550/arxiv.0711.1897

arxiv created 2007/11/13 · arxiv updated 2009/12/01

Abstract

The 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.

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