Inversion formulas for the spherical mean transform with data on an ellipsoid in two and three dimensions

This presentation is devoted to the problem of
recovering a function from its spherical means with
centers located on an ellipsoid $\Sigma$ in the two- and
three-dimensional spaces. We will show how to
generalize methods for obtaining inverse
formulas for the case when $\Sigma$ is a sphere to the
case when $\Sigma$ is an ellipsoid.