ABSTRACT
This chapter provides a range characterization result for the plane-to-line transform on R3, in terms of the ultrahyperbolic equations of Fritz John. This equation was used to characterize the range of the X-ray transform on rapidly decreasing functions on R3, and has the feature of being invariant under the group of orientation-preserving rigid motions of R3. The chapter explains plane-to-line transform in the harmonic analysis and integral geometry. It aims to characterize the range of R using John’s ultrahyperbolic differential equation on the line space.
