The point source inverse back-scattering problem

Rakesh; Gunther Uhlmann

doi:10.1090/conm/644/12784

The point source inverse back-scattering problem

Rakesh, Gunther Uhlmann

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

6 Citations (Scopus)

Abstract

We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is similar to the inverse backscattering problem. We show that if the angular derivatives of the difference of two potentials having the same data is controlled by the L²norm of the difference of the potentials they must be equal. In particular this shows injectivity of the inverse problem for radial potentials.

Original language	English
Title of host publication	Contemporary Mathematics
Publisher	American Mathematical Society
Pages	279-289
Number of pages	11
DOIs	https://doi.org/10.1090/conm/644/12784
Publication status	Published - 2015
Externally published	Yes

Publication series

Name	Contemporary Mathematics
Volume	644
ISSN (Print)	0271-4132
ISSN (Electronic)	1098-3627

Bibliographical note

Publisher Copyright:
© 2015 American Mathematical Society.

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10.1090/conm/644/12784

Cite this

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abstract = "We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is similar to the inverse backscattering problem. We show that if the angular derivatives of the difference of two potentials having the same data is controlled by the L2norm of the difference of the potentials they must be equal. In particular this shows injectivity of the inverse problem for radial potentials.",

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AB - We consider the inverse problem of recovering a potential by measuring the response at a point to a source located at the same point and then varying the point on the surface of a sphere. This is similar to the inverse backscattering problem. We show that if the angular derivatives of the difference of two potentials having the same data is controlled by the L2norm of the difference of the potentials they must be equal. In particular this shows injectivity of the inverse problem for radial potentials.

UR - https://openalex.org/W2138198354

UR - https://www.scopus.com/pages/publications/84963865778

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BT - Contemporary Mathematics

PB - American Mathematical Society

ER -

The point source inverse back-scattering problem

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