Algebraically integrable bodies and related properties of the Radon transform

Mark Agranovsky, Jan Boman, Alexander Koldobsky, Victor Vassiliev, Vladyslav Yaskin

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


Generalizing Lemma 28 from Newton's "Principia" [25], Arnold [10] asked for a complete characterization of algebraically integrable domains. In this chapter we describe the current state of Arnold's problems. We also consider closely related problems involving the Radon transform of indicator functions.

Original languageEnglish
Title of host publicationHarmonic Analysis and Convexity
Publisherde Gruyter
Number of pages36
ISBN (Electronic)9783110775389
ISBN (Print)9783110775372
StatePublished - 24 Jul 2023

Bibliographical note

Publisher Copyright:
© 2023 Walter de Gruyter GmbH, Berlin/Boston. All rights reserved.


  • Analytic continuation
  • Convex body
  • Fourier transform
  • Integrability
  • Monodromy
  • Picard-Lefschetz theory
  • Radon transform


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