Geodesic
A Support Theorem for the Complex Radon Transform of Distributions
Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 719-727 
A. B. Sekerin. A Support Theorem for the Complex Radon Transform of Distributions. Matematičeskie zametki, Tome 74 (2003) no. 5, pp. 719-727. http://geodesic.mathdoc.fr/item/MZM_2003_74_5_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The properties of the complex Radon transform of compactly supported distributions are considered. For such distributions, we prove a support theorem allowing us to describe the support of the distribution in terms of the support of its Radon transform.

[1] Gelfand I. M., Graev M. I., Vilenkin N. Ya., Integralnaya geometriya i svyazannye s nei voprosy teorii predstavlenii, Nauka, M., 1962

[2] Khelgason S., Preobrazovanie Radona, Mir, M., 1983

[3] Ludwig D., “The Radon transform on Euclidean space”, Comm. Pure Appl. Math., 19 (1966), 49–81 | DOI | MR | Zbl

[4] Sekerin A. B., “A support theorem for the complex Radon transform”, Collectanea Mathematica, 50 (1999), 221–227 | MR | Zbl

[5] Sekerin A. B., Primeneniya preobrazovaniya Radona v teorii approksimatsii, Bashkirsk. nauchn. tsentr UrO AN SSSR, Ufa, 1991

[6] Hertle A., “Continuity of the Radon transform and its inverse on Euclidean spaces”, Math. Zeitschr., 184 (1983), 165–192 | DOI | MR

[7] Sekerin A. B., Primenenie preobrazovaniya Radona k approksimatsionnym zadacham mnogomernogo kompleksnogo analiza, Diss. $\dots$ d.f.-m.n., In-t matematiki UrO RAN, Ufa, 1992

[8] Sekerin A. B., “Representation of functions by logarithmic potentials and reducibility of analytic functions of several variables”, Collectanea Mathematica, 47 (1996), 187–206 | MR | Zbl

[9] Khermander L., Teoriya raspredelenii i analiz Fure, Mir, M., 1986