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ON DETERMINATION OF A GAUGE FIELD ON ℝd FROM ITS NON-ABELIAN RADON TRANSFORM ALONG ORIENTED STRAIGHT LINES

Published online by Cambridge University Press:  14 October 2002

R. G. Novikov
R. G. Novikov
Affiliation:
CNRS, UMR 6629, Département de Mathématiques, Université de Nantes, BP 92208, F-44322, Nantes cedex 03, France (novikov@math.univ-nantes.fr)
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Abstract

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We consider the inverse connection problem consisting of determining a gauge field on $\mathbb{R}^d$ from its non-abelian Radon transform along oriented straight lines. The determination is considered modulo gauge transformations. Our results include: 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 to the attenuated X-ray transform.

AMS 2000 Mathematics subject classification: Primary 53C65; 81U40

Keywords

gauge fieldnon-abelian Radon transforminverse connection problem
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 1 , Issue 4 , October 2002 , pp. 559 - 629
Copyright
2002 Cambridge University Press