Range characterizations and Singular Value Decomposition of the geodesic X-ray transform on disks of constant curvature

Mishra, Rohit KumarRohit KumarMishraMonard, FrançoisFrançoisMonard2025-08-312025-08-312021-01-0110.4171/JST/3642-s2.0-85116759025https://d8.irins.org/handle/IITG2025/25613For a one-parameter family of simple metrics of constant curvature (4 for 2 .-1; 1/) on the unit disk M, we first make explicit the Pestov-Uhlmann range characterization of the geodesic X-ray transform, by constructing a basis of functions making up its range and co-kernel. Such a range characterization also translates into moment conditions à la Helgason-Ludwig or Gel'fand-Graev. We then derive an explicit Singular Value Decomposition for the geodesic X-ray transform. Computations dictate a specific choice of weighted L2-L2 setting which is equivalent to the L2.M; dVol / ! L2.@CSM; d 2/ one for any 2 .-1; 1/.trueConsistency conditions | Constant curvature | Geodesic X-ray transform | Integral geometry | Inverse problems | Range characterization | SingularValue DecompositionRange characterizations and Singular Value Decomposition of the geodesic X-ray transform on disks of constant curvatureArticlehttps://ems.press/content/serial-article-files/12504166404031005-104120215arJournal5WOS:000704993600005