On a Stability Property of the Generalized Spherical Radon Transform

Dmitry Faifman

doi:10.1007/978-1-4614-6406-8_5

On a Stability Property of the Generalized Spherical Radon Transform

Dmitry Faifman^*

^*Corresponding author for this work

School of Mathematical Sciences

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

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 language	English
Title of host publication	Asymptotic Geometric Analysis
Subtitle of host publication	Proceedings of the Fall 2010 Fields Institute Thematic Program
Editors	Monika Ludwig, Vladimir Pestov, Vitali Milman, Nicole Tomczak-Jaegermann
Publisher	Springer New York
Pages	55-73
Number of pages	19
ISBN (Print)	9781461464051
DOIs	https://doi.org/10.1007/978-1-4614-6406-8_5
State	Published - 2013

Publication series

Name	Fields Institute Communications
Volume	68
ISSN (Print)	1069-5265

Keywords

Integral geometry
Pseudodifferential operators
Radon transform
Sobolev spaces

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10.1007/978-1-4614-6406-8_5

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Faifman, D. (2013). On a Stability Property of the Generalized Spherical Radon Transform. In M. Ludwig, V. Pestov, V. Milman, & N. Tomczak-Jaegermann (Eds.), Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program (pp. 55-73). (Fields Institute Communications; Vol. 68). Springer New York. https://doi.org/10.1007/978-1-4614-6406-8_5

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On a Stability Property of the Generalized Spherical Radon Transform. / Faifman, Dmitry.
Asymptotic Geometric Analysis: Proceedings of the Fall 2010 Fields Institute Thematic Program. ed. / Monika Ludwig; Vladimir Pestov; Vitali Milman; Nicole Tomczak-Jaegermann. Springer New York, 2013. p. 55-73 (Fields Institute Communications; Vol. 68).

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

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KW - Pseudodifferential operators

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On a Stability Property of the Generalized Spherical Radon Transform

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