Algebraically integrable bodies and related properties of the Radon transform

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

doi:10.1515/9783110775389-001

Algebraically integrable bodies and related properties of the Radon transform

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

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

2 Scopus citations

Abstract

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 language	English
Title of host publication	Harmonic Analysis and Convexity
Publisher	de Gruyter
Pages	1-36
Number of pages	36
ISBN (Electronic)	9783110775389
ISBN (Print)	9783110775372
DOIs	https://doi.org/10.1515/9783110775389-001
State	Published - 24 Jul 2023

Bibliographical note

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

Keywords

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

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10.1515/9783110775389-001

Cite this

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KW - Convex body

KW - Fourier transform

KW - Integrability

KW - Monodromy

KW - Picard-Lefschetz theory

KW - Radon transform

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Algebraically integrable bodies and related properties of the Radon transform

Abstract

Bibliographical note

Keywords

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