The Reshetnyak formula and Natterer stability estimates in tensor tomography Full article
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Inverse Problems
ISSN: 0266-5611 |
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| Output data | Year: 2017, Volume: 33, Number: 2, Article number : 025002, Pages count : DOI: 10.1088/1361-6420/33/2/025002 | ||||
| Tags | Reshetnyak formula; stability estimates; tensor tomography | ||||
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Abstract:
The Reshetnyak formula (also known as the Plancherel formula for the Radon transform) states that the Radon transform R is an isometry between and , the latter being the Hilbert space of even functions on furnished by some special norm. We generalize this statement to Sobolev spaces: R is an isometry between and for every real s. Moreover, with the help of Riesz potentials, we define some new Hilbert spaces and prove that R is an isometry between and . The generalized Reshetnyak formula closely relates to the Natterer stability estimates: for functions f supported in a fixed ball. Then we obtain analogs of these statements for the x-ray transform of symmetric tensor fields. © 2016 IOP Publishing Ltd.
Cite:
Sharafutdinov V.A.
The Reshetnyak formula and Natterer stability estimates in tensor tomography
Inverse Problems. 2017. V.33. N2. 025002 . DOI: 10.1088/1361-6420/33/2/025002 WOS Scopus OpenAlex
The Reshetnyak formula and Natterer stability estimates in tensor tomography
Inverse Problems. 2017. V.33. N2. 025002 . DOI: 10.1088/1361-6420/33/2/025002 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000391708600001 |
| Scopus: | 2-s2.0-85010664819 |
| OpenAlex: | W2565137333 |