DOI QR코드

DOI QR Code

GLOBAL UNIQUENESS FOR THE RADON TRANSFORM

  • Received : 2019.03.07
  • Accepted : 2020.03.31
  • Published : 2020.05.31

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 ∈ L1 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.

References

  1. N. U. Arakeljan, Uniform approximation on closed sets by entire functions, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1187-1206.
  2. D. H. Armitage, A non-constant continuous function on the plane whose integral on every line is zero, Amer. Math. Monthly 101 (1994), no. 9, 892-894. https://doi.org/10.2307/2975138
  3. A. Kaneko, Introduction to Hyperfunctions, translated from the Japanese by Y. Yamamoto, Mathematics and its Applications (Japanese Series), 3, Kluwer Academic Publishers Group, Dordrecht, 1988.
  4. T. Takiguchi, Remarks on modification of Helgason's support theorem. II, Proc. Japan Acad. Ser. A Math. Sci. 77 (2001), no. 6, 87-91, loose errata. http://projecteuclid.org/euclid.pja/1148479941
  5. T. Takiguchi and A. Kaneko, Radon transform of hyperfunctions and support theorem, Hokkaido Math. J. 24 (1995), no. 1, 63-103. https://doi.org/10.14492/hokmj/1380892536
  6. L. Zalcman, Uniqueness and nonuniqueness for the Radon transform, Bull. London Math. Soc. 14 (1982), no. 3, 241-245. https://doi.org/10.1112/blms/14.3.241