Non-central Funk-Radon transforms: Single and multiple

Mark Agranovsky

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We study Funk-type transforms associated with intersections of the unit sphere in Rn with lower-dimensional affine planes passing through a given point inside or outside the sphere. Our goal is to investigate injectivity of such “paired” transforms generated by two families of planes centered at distinct points. Necessary and sufficient conditions of injectivity are obtained in terms of geometry of the centers location. The technique used is based upon the action of the automorphism group of the unit ball and a related billiard-like dynamics on the sphere.

Original languageEnglish
Article number108701
JournalJournal of Functional Analysis
Issue number8
StatePublished - 1 Nov 2020

Bibliographical note

Publisher Copyright:
© 2020 Elsevier Inc.


  • Dynamics
  • Funk transform
  • Injectivity
  • Möbius transformations


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