ON DETERMINATION OF A GAUGE FIELD ON ℝd FROM ITS NON-ABELIAN RADON TRANSFORM ALONG ORIENTED STRAIGHT LINES
| Autor: | R. G. Novikov |
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| Rok vydání: | 2002 |
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| Zdroj: | Journal of the Institute of Mathematics of Jussieu. 1:559-629 |
| ISSN: | 1475-3030 1474-7480 |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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