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.