8,594 research outputs found
Extending the Support Theorem to Infinite Dimensions
The Radon transform is one of the most useful and applicable tools in
functional analysis. First constructed by John Radon in 1917 it has now been
adapted to several settings. One of the principle theorems involving the Radon
transform is the Support Theorem. In this paper, we discuss how the Radon
transform can be constructed in the white noise setting. We also develop a
Support Theorem in this setting.Comment: 22 page
Trkalian fields and Radon transformation
We write the spherical curl transformation for Trkalian fields using
differential forms. Then we consider Radon transform of these fields. The Radon
transform of a Trkalian field satisfies a corresponding eigenvalue equation on
a sphere in transform space. The field can be reconstructed using knowledge of
the Radon transform on a canonical hemisphere. We consider relation of the
Radon transformation with Biot-Savart integral operator and discuss its
transform introducing Radon-Biot- Savart operator. The Radon transform of a
Trkalian field is an eigenvector of this operator. We also present an Ampere
law type relation for these fields. We apply these to Lundquist solution. We
present a Chandrasekhar-Kendall type solution of the corresponding equation in
the transform space. Lastly, we focus on the Euclidean topologically massive
Abelian gauge theory. The Radon transform of an anti-self-dual field is related
by antipodal map on this sphere to the transform of the self-dual field
obtained by inverting space coordinates. The Lundquist solution provides an
example of quantization of topological mass in this context.Comment: 23 page
On Y. Nievergelt's inversion formula for the Radon transform
We generalize Y. Nievergelt's inversion method for the Radon transform on
lines in the 2-plane to the -plane Radon transform of continuous and
functions on for all .Comment: 9 page
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