Bull. Korean Math. Soc. 2020; 57(3): 597-605
Online first article May 7, 2020 Printed May 31, 2020
https://doi.org/10.4134/BKMS.b190253
Copyright © The Korean Mathematical Society.
Takashi Takiguchi
National Defense Academy of Japan
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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