Showing papers by "Gregory Beylkin published in 1988"
TL;DR: In this paper, the authors derived a relation between differential forms on the space Sn-1*Sn-1 and those on I*sn-2*Sn1, where I is a real interval, and derived the results of John relating the iterated spherical mean of a function to its spherical mean.
Abstract: Formulae involving double integrals over spheres arise naturally in inverse scattering problems since the scattered data are measured in the space R*S2*S2. The authors derive a relation between differential forms on the space Sn-1*Sn-1, and those on the space I*Sn-2*Sn-1, where I is a real interval. Specifically, d xi d eta =sinn-2 theta d theta d psi d nu ( xi , eta ) in Sn-1*Sn-1 and ( theta , psi , nu ) in I*Sn-2*Sn-1. This allows them to derive the results of John relating the iterated spherical mean of a function to its spherical mean in a simple way; to obtain new inversion formulae for the Fourier and Radon transforms; to extend formulae for linearised inverse quantum scattering and diffraction tomography to the multifrequency case; and also to establish a relation between multifrequency diffraction tomography and seismic migration algorithms.
28 citations