Nonuniqueness for the Radon transform
HTML articles powered by AMS MathViewer
- by D. H. Armitage and M. Goldstein PDF
- Proc. Amer. Math. Soc. 117 (1993), 175-178 Request permission
Abstract:
There exists a nonconstant harmonic function $h$ on ${\mathbb {R}^N}$, where $N \geqslant 2$, such that ${\smallint _P}|h| < + \infty$ and ${\smallint _P}h = 0$ for every $(N - 1)$-dimensional hyperplane $P$.References
- N. U. Arakeljan, Uniform approximation on closed sets by entire functions, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1187–1206 (Russian). MR 0170017
- D. H. Armitage and S. J. Gardiner, The growth of the hyperplane mean of a subharmonic function, J. London Math. Soc. (2) 36 (1987), no. 3, 501–512. MR 918641, DOI 10.1112/jlms/s2-36.3.501
- D. H. Armitage and M. Goldstein, Better than uniform approximation on closed sets by harmonic functions with singularities, Proc. London Math. Soc. (3) 60 (1990), no. 2, 319–343. MR 1031456, DOI 10.1112/plms/s3-60.2.319
- Sigurdur Helgason, The Radon transform, 2nd ed., Progress in Mathematics, vol. 5, Birkhäuser Boston, Inc., Boston, MA, 1999. MR 1723736, DOI 10.1007/978-1-4757-1463-0
- Lawrence Zalcman, Uniqueness and nonuniqueness for the Radon transform, Bull. London Math. Soc. 14 (1982), no. 3, 241–245. MR 656606, DOI 10.1112/blms/14.3.241
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 117 (1993), 175-178
- MSC: Primary 44A12; Secondary 92C55
- DOI: https://doi.org/10.1090/S0002-9939-1993-1106177-3
- MathSciNet review: 1106177