Momentum ray transforms, II: Range characterization in the Schwartz space

Venkateswaran P. Krishnan, Ramesh Manna, Suman Kumar Sahoo, Vladimir A. Sharafutdinov

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

The momentum ray transform I k integrates a rank m symmetric tensor field f  over lines of with the weight t k: We give the range characterization for the operator on the Schwartz space of rank m smooth fast decaying tensor fields. In dimensions, the range is characterized by certain differential equations of order which generalize the classical John equations. In the two-dimensional case, the range is characterized by certain integral conditions which generalize the classical Gelfand-Helgason-Ludwig conditions.

Original languageEnglish
Article number045009
Number of pages33
JournalInverse Problems
Volume36
Issue number4
DOIs
Publication statusPublished - Apr 2020

Keywords

  • inverse problems
  • John's conditions
  • momentum ray transform
  • range characterization
  • ray transform
  • tensor analysis

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