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Proceedings of the American Mathematical Society

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

 

 

Analytic multipliers of the Radon transform


Author: James V. Peters
Journal: Proc. Amer. Math. Soc. 72 (1978), 485-491
MSC: Primary 44A15; Secondary 43A85
MathSciNet review: 509239
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Abstract: We define the Radon transform over the real and complex domain, and list some of its simplest properties. For the complex domain $ {{\mathbf{C}}^n}$, a theorem of the Paley-Wiener type is obtained to determine the support of a continuous, integrable function from its Radon transform. The construction requires defining an associated function of the Radon transform for each $ z \in {{\mathbf{C}}^n}$. The support of the function is then obtained via analytic multipliers of the associated functions.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0509239-6
Keywords: Radon transform, support, analytic multipliers
Article copyright: © Copyright 1978 American Mathematical Society