Bulletin of the
Korean Mathematical Society BKMS

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.