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A new proof of the support theorem and the range characterization for the Radon transform
Bernd Drostesubject
Pure mathematicsFactor theoremRadon transformGeneral MathematicsProjection-slice theoremMathematical analysisElementary proofFourier inversion theoremBrouwer fixed-point theoremRadon's theoremShift theoremMathematicsdescription
The aim of this note is to give a new and elementary proof of the support theorem for the Radon transform, which is based only on the projection theorem and the Paley-Wiener theorem for the Fourier transform. The idea is to solve a certain system of linear equations in order to determine the coefficients of a homogeneous polynomial (interpolation problem). By the same method, we get a short proof of the range characterization for Radon transforms of functions supported in a ball.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1983-06-01 | Manuscripta Mathematica |