Abstract
The support theorem for the Radon transform was obtained by L. Helgason. The Radon transform of functions of variables related by spherical symmetry is a special case of a more general transformation, namely, the Radon–Kipriyanov transform K𝛾. This transformation corresponds to a weight multi-index 𝛾 = (𝛾1, . . . , 𝛾m) and coincides with the Radon transform if all components of the multi-index 𝛾 are natural numbers. In general, the K𝛾-transformation can be interpreted as a transformation of functions of a fraction-dimensional argument. In this paper, we prove a general support theorem. In a special case where 𝛾 = 0, this theorem coincides with the Helgason theorem.
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