On a Stability Property of the Generalized Spherical Radon Transform

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Abstract

In this note, we study the operator norm of the generalized spherical Radon transform, defined by a smooth measure on the underlying incidence variety. In particular, we prove that for small perturbations of the measure, the spherical Radon transform remains an isomorphism between the corresponding Sobolev spaces.

Original languageEnglish
Title of host publicationAsymptotic Geometric Analysis
Subtitle of host publicationProceedings of the Fall 2010 Fields Institute Thematic Program
EditorsMonika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann
PublisherSpringer New York
Pages55-73
Number of pages19
ISBN (Print)9781461464051
DOIs
StatePublished - 2013

Publication series

NameFields Institute Communications
Volume68
ISSN (Print)1069-5265

Keywords

  • Integral geometry
  • Pseudodifferential operators
  • Radon transform
  • Sobolev spaces

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