Support Theorems for the Radon Transform and Cramér-Wold Theorems |
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Authors: | Jan Boman Filip Lindskog |
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Institution: | (1) Department of Mathematics, Stockholm University, 10691 Stockholm, Sweden;(2) Department of Mathematics, Royal Institute of Technology, 10044 Stockholm, Sweden |
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Abstract: | This article presents extensions of the Cramér-Wold theorem to measures that may have infinite mass near the origin. Corresponding
results for sequences of measures are presented together with examples showing that the assumptions imposed are sharp. The
extensions build on a number of results and methods concerned with injectivity properties of the Radon transform. Using a
few tools from distribution theory and Fourier analysis we show that the presented injectivity results for the Radon transform
lead to Cramér-Wold type results for measures. One purpose of this article is to contribute to making known to probabilists
interesting results for the Radon transform that have been developed essentially during the 1980s and 1990s. |
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Keywords: | Cramér-Wold theorem Radon transform |
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