Affiliation:
1. Department of Mathematics , Stockholm University , Stockholm , Sweden
Abstract
Abstract
If the Radon transform of a compactly supported distribution
f
≠
0
{f\neq 0}
in
ℝ
n
{\mathbb{R}^{n}}
is supported on the set of tangent planes to the boundary
∂
D
{\partial D}
of a bounded convex domain D, then
∂
D
{\partial D}
must be an ellipsoid. The special case of this result when the domain D is symmetric was treated in
[J. Boman,
A hypersurface containing the support of a Radon transform must be an ellipsoid. I: The symmetric case,
J. Geom. Anal. 2020, 10.1007/s12220-020-00372-8].
Here we treat the general case.
Reference6 articles.
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A local uniqueness theorem for weighted Radon transforms,
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A hypersurface containing the support of a Radon transform must be an ellipsoid. I: The symmetric case,
J. Geom. Anal. (2020), 10.1007/s12220-020-00372-8.
3. S. Helgason,
The Radon Transform,
Birkhäuser, Stuttgart, 1980.
4. L. Hörmander,
The Analysis of Linear Partial Differential Operators. I,
Springer, Berlin, 1983.
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The Mathematics of Computerized Tomography,
Teubner, Stuttgart, 1986.
Cited by
3 articles.
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