Global uniqueness for the Radon transform
Bull. Korean Math. Soc. 2020 Vol. 57, No. 3, 597-605
https://doi.org/10.4134/BKMS.b190253
Published online May 31, 2020
Takashi Takiguchi
National Defense Academy of Japan
Abstract : In this article, we discuss the global uniqueness problem for the Radon transform. It is not sufficient for the global uniqueness for the Radon transform to assume that the Radon transform $Rf$ for a function $f$ absolutely converges on any hyperplane. It is also known that it is sufficient to assume that $f \in L^1$ for the global uniqueness to hold. There exists a big gap between the above two conditions, to fill which is our purpose in this paper. We shall give a better sufficient condition for the global uniqueness of the Radon transform.
Keywords : The Radon transform, holomorphic functions, hyperfunctions
MSC numbers : 44A12, 46F15, 46F20
Supported by : The author was supported in part by JSPS Grant-in-Aid for Scientific Research (C) 26400184.
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