Range characterizations and Singular Value Decomposition of the geodesic X-ray transform on disks of constant curvature
Rohit Kumar Mishra
Indian Institute of Technology Gandhinagar, IndiaFrançois Monard
University of California, Santa Cruz, USA
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Abstract
For a one-parameter family of simple metrics of constant curvature ( for ) on the unit disk , 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 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 setting which is equivalent to the one for any .
Cite this article
Rohit Kumar Mishra, François Monard, Range characterizations and Singular Value Decomposition of the geodesic X-ray transform on disks of constant curvature. J. Spectr. Theory 11 (2021), no. 3, pp. 1005–1041
DOI 10.4171/JST/364