On determination of a gauge field on d from its non-abelian radon transform along oriented straight lines

R. G. Novikov

doi:10.1017/S1474748002000166

On determination of a gauge field on d from its non-abelian radon transform along oriented straight lines

R. G. Novikov

Université de Nantes

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Résumé

We consider the inverse connection problem consisting of determining a gauge field on from its non-abelian Radontransform along oriented straight lines. The determination is considered modulo gauge transformations. Our resultsinclude: global uniqueness theorems for d\geq3, new local uniqueness theorems for d=2, constructive proofs(i.e. proofs containing reconstruction procedures), counterexamples to the global uniqueness for d=2, a reduction tothe attenuated X-ray transform.

langue originale	Anglais
Pages (de - à)	559-629
Nombre de pages	71
journal	Journal of the Institute of Mathematics of Jussieu
Volume	1
Numéro de publication	4
Les DOIs	https://doi.org/10.1017/S1474748002000166
état	Publié - 1 janv. 2002
Modification externe	Oui

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10.1017/S1474748002000166

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title = "On determination of a gauge field on d from its non-abelian radon transform along oriented straight lines",

abstract = "We consider the inverse connection problem consisting of determining a gauge field on from its non-abelian Radontransform along oriented straight lines. The determination is considered modulo gauge transformations. Our resultsinclude: global uniqueness theorems for d\textbackslash{}geq3, new local uniqueness theorems for d=2, constructive proofs(i.e. proofs containing reconstruction procedures), counterexamples to the global uniqueness for d=2, a reduction tothe attenuated X-ray transform.",

keywords = "gauge field, inverse connection problem, non-abelian Radon transform",

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N2 - We consider the inverse connection problem consisting of determining a gauge field on from its non-abelian Radontransform along oriented straight lines. The determination is considered modulo gauge transformations. Our resultsinclude: global uniqueness theorems for d\geq3, new local uniqueness theorems for d=2, constructive proofs(i.e. proofs containing reconstruction procedures), counterexamples to the global uniqueness for d=2, a reduction tothe attenuated X-ray transform.

AB - We consider the inverse connection problem consisting of determining a gauge field on from its non-abelian Radontransform along oriented straight lines. The determination is considered modulo gauge transformations. Our resultsinclude: global uniqueness theorems for d\geq3, new local uniqueness theorems for d=2, constructive proofs(i.e. proofs containing reconstruction procedures), counterexamples to the global uniqueness for d=2, a reduction tothe attenuated X-ray transform.

KW - gauge field

KW - inverse connection problem

KW - non-abelian Radon transform

U2 - 10.1017/S1474748002000166

DO - 10.1017/S1474748002000166

M3 - Article

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SP - 559

EP - 629

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

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ER -

On determination of a gauge field on d from its non-abelian radon transform along oriented straight lines

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