2017/05/16 by Salman, Yehonatan
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.1705.05679
The aim of this paper is to introduce a new inversion procedure for re- covering functions, defined on \Bbb R2, from the spherical mean transform, which integrates functions on a prescribed family Λ of circles, where Λ consists of circles whose centers belong to a given ellipse E on the plane. The method presented here follows the same procedure which was used by S. J. Norton in [22] for recovering functions in case where Λ consists of circles with centers on a circle. However, at some point we will have to modify the method in [22] by using expansion in elliptical coordinates, rather than spherical coordinates, in order to solve the more generalized elliptical case. We will rely on a recent result obtained by H.S. Cohl and H.Volkmer in [8] for the eigenfunction expansion of the Bessel function in elliptical coordinates.