by Joonas Ilmavirta
Abstract:
We show injectivity of the X-ray transform and the $d$-plane Radon transform for distributions on the $n$-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvi\`ere.
We also show solenoidal injectivity of the X-ray transform on the $n$-torus for tensor fields of any order, allowing the tensors to have distribution valued coefficients.
These imply new injectivity results for the periodic broken ray transform on cubes of any dimension.
Reference:
On Radon transforms on tori (Joonas Ilmavirta), Journal of Fourier Analysis and Applications, volume 21, number 2, pp. 370–382, 2015.
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We show injectivity of the X-ray transform and the $d$-plane Radon transform for distributions on the $n$-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvière.
We also show solenoidal injectivity of the X-ray transform on the $n$-torus for tensor fields of any order, allowing the tensors to have distribution valued coefficients.
These imply new injectivity results for the periodic broken ray transform on cubes of any dimension.
[arXiv]
Bibtex Entry:
@article{torus,
author = {Joonas Ilmavirta},
title = {{On Radon transforms on tori}},
journal = {Journal of Fourier Analysis and Applications},
year={2015},
issn={1069-5869},
volume={21},
number={2},
pages={370--382},
arxiv = {1402.6209},
doi = {10.1007/s00041-014-9374-x},
url={http://users.jyu.fi/~jojapeil/pub/torus.pdf},
gsid = {18417540735791649700},
abstract = {We show injectivity of the X-ray transform and the $d$-plane Radon transform for distributions on the $n$-torus, lowering the regularity assumption in the recent work by Abouelaz and Rouvi\`ere.
We also show solenoidal injectivity of the X-ray transform on the $n$-torus for tensor fields of any order, allowing the tensors to have distribution valued coefficients.
These imply new injectivity results for the periodic broken ray transform on cubes of any dimension.}
}