The hyperbolic X-ray transform: new range characterizations, mapping properties and functional relations

We derive new singular value decompositions and range characterizations for the X-ray transform on the Poincar\'e disk, intertwining relations with distinguished differential operators of wedge type, and a surjectivity result for the backprojection operator. New functional settings are found, which allow to sharply understand boundary behavior issues and invertibility settings. The approach mainly exploits analogous results obtained only recently in the Euclidean disk, together with the projective equivalence between the two models.