Analytic multipliers of the Radon transform

Peters, James V.

doi:10.1090/S0002-9939-1978-0509239-6

Analytic multipliers of the Radon transform
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by James V. Peters PDF

Proc. Amer. Math. Soc. 72 (1978), 485-491 Request permission

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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