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

Research output: Contribution to journal › Article › peer-review

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\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.

Original language	English
Pages (from-to)	559-629
Number of pages	71
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	1
Issue number	4
DOIs	https://doi.org/10.1017/S1474748002000166
Publication status	Published - 1 Jan 2002
Externally published	Yes

Keywords

gauge field
inverse connection problem
non-abelian Radon transform

Access to Document

10.1017/S1474748002000166

Cite this

@article{92621d26512d49ec958f2c4099d54d82,

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",

author = "Novikov, \{R. G.\}",

year = "2002",

month = jan,

day = "1",

doi = "10.1017/S1474748002000166",

language = "English",

volume = "1",

pages = "559--629",

journal = "Journal of the Institute of Mathematics of Jussieu",

issn = "1474-7480",

number = "4",

}

TY - JOUR

T1 - On determination of a gauge field on d from its non-abelian radon transform along oriented straight lines

AU - Novikov, R. G.

PY - 2002/1/1

Y1 - 2002/1/1

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

AN - SCOPUS:11044227931

SN - 1474-7480

VL - 1

SP - 559

EP - 629

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

IS - 4

ER -

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this