On an operator associated to a restricted x -ray transform

摘要

For the restricted x-ray transform RC we study the composite operator RtC&j0;RC . We find the wavefront set of the operator and verify the flowout structure of the set of singularities. Using the Theory of Fourier Integral Operators we are able to compute the symbols of the operator and understand what sort of singularities the operator can detect and what it can not. With these symbols this paper gives the resulting symbols when the operator is applied on the conormal distributions of some smooth surfaces. Applying on conormal distribution we could also determine the image class of distributions based on the initial class of conormal distributions.