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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Nonuniqueness for the Radon transform


Authors: D. H. Armitage and M. Goldstein
Journal: Proc. Amer. Math. Soc. 117 (1993), 175-178
MSC: Primary 44A12; Secondary 92C55
MathSciNet review: 1106177
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Abstract: There exists a nonconstant harmonic function $ h$ on $ {\mathbb{R}^N}$, where $ N \geqslant 2$, such that $ {\smallint _P}\vert h\vert < + \infty $ and $ {\smallint _P}h = 0$ for every $ (N - 1)$-dimensional hyperplane $ P$.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1106177-3
Keywords: Radon transform, harmonic function
Article copyright: © Copyright 1993 American Mathematical Society