ABSTRACT
This chapter considers the problem of integral geometry in a three-dimensional layer on a family of paraboloids with perturbation which represents the integral over the interior of the paraboloids with a known weight function. It provides a uniqueness theorem for this problem under rather general assumptions on the weight function. The chapter shows that the uniqueness question for the problem of integral geometry of rather general form reduces to the studying uniqueness of solutions of the operator equation. It examines a uniqueness theorem for the general Volterra-type problem of integral geometry. The chapter presents the formulation of the general Volterra-type problem of integral geometry in the three-dimensional space. Problems of integral geometry arise in a natural way in the study of many mathematical models in domains having extensive applications, such as seismic prospecting, interpretation of the data of geophysical and aerospace observations, and various processes described by kinetic equations.
