On a Generalization of Exponential Ray Transform in Tomography

We consider the operator of generalized exponential ray transform whose values are the initial data in the emission computer tomography problem. We establish connections between exponential ray transforms of different orders and obtain the differential equations satisfied by the exponential ray transforms. We prove the uniqueness theorems for boundary value and initial-boundary value problems for the corresponding equations We also discuss close connections of generalized exponential ray transforms with integral geometry of tensor fields and tomography problems.