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A Support Theorem for the Complex Radon Transform of Distributions

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Abstract

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.

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REFERENCES

  1. I. M. Gel'fand, M. I. Graev, and N. Ya. Vilenkin, Integral Geometry and Related Problems of Representation Theory [in Russian] Nauka, Moscow, 1962.

    Google Scholar 

  2. S. Helgason, The Radon Transform, Birkhäuser, Boston, 1980; Russian translation: Mir, Moscow, 1983.

    Google Scholar 

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

    Google Scholar 

  4. A. B. Sekerin, “A support theorem for the complex Radon transform, ” Collectanea mathematica, 50 (1999), 221–227.

    Google Scholar 

  5. A. B. Sekerin, Applications of the Radon transform to Approximation Theory [in Russian], Bashkir Scientific Center of the Ural Division of the Academy of Sciences of the USSR, Ufa, 1991.

    Google Scholar 

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

    Google Scholar 

  7. A. B. Sekerin, Application of the Radon transform to Approximation Problems of Multidimensional Complex Analysis, Doctoral (Phys.–Math.) Dissertation, Ural Division of the Academy of Sciences of the USSR, Ufa, 1992.

    Google Scholar 

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

    Google Scholar 

  9. L. Hörmander, The Analysis of Linear Partial Differential Operators, vol. 2, Springer-Verlag, Heidelberg, 1983; Russian translation: Mir, Moscow, 1986.

    Google Scholar 

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Authors and Affiliations

  1. Orlov State University, Russia

    A. B. Sekerin

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  1. A. B. Sekerin
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Sekerin, A.B. A Support Theorem for the Complex Radon Transform of Distributions. Mathematical Notes 74, 676–684 (2003). https://doi.org/10.1023/B:MATN.0000009000.71463.55

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  • DOI: https://doi.org/10.1023/B:MATN.0000009000.71463.55

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