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The Reshetnyak formula and Natterer stability estimates in tensor tomography. / Sharafutdinov, Vladimir A.

In: Inverse Problems, Vol. 33, No. 2, 025002, 01.02.2017.

Research output: Contribution to journal › Article › peer-review

Harvard

Sharafutdinov, VA 2017, 'The Reshetnyak formula and Natterer stability estimates in tensor tomography', Inverse Problems, vol. 33, no. 2, 025002. https://doi.org/10.1088/1361-6420/33/2/025002

APA

Sharafutdinov, V. A. (2017). The Reshetnyak formula and Natterer stability estimates in tensor tomography. Inverse Problems, 33(2), [025002]. https://doi.org/10.1088/1361-6420/33/2/025002

Vancouver

Sharafutdinov VA. The Reshetnyak formula and Natterer stability estimates in tensor tomography. Inverse Problems. 2017 Feb 1;33(2):025002. doi: 10.1088/1361-6420/33/2/025002

Author

Sharafutdinov, Vladimir A. / The Reshetnyak formula and Natterer stability estimates in tensor tomography. In: Inverse Problems. 2017 ; Vol. 33, No. 2.

BibTeX

@article{bbf99c70046448d997753deebb471faf,
title = "The Reshetnyak formula and Natterer stability estimates in tensor tomography",
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.",
keywords = "Reshetnyak formula, stability estimates, tensor tomography, SPACE",
author = "Sharafutdinov, {Vladimir A.}",
year = "2017",
month = feb,
day = "1",
doi = "10.1088/1361-6420/33/2/025002",
language = "English",
volume = "33",
journal = "Inverse Problems",
issn = "0266-5611",
publisher = "IOP Publishing Ltd.",
number = "2",

}

RIS

TY - JOUR

T1 - The Reshetnyak formula and Natterer stability estimates in tensor tomography

AU - Sharafutdinov, Vladimir A.

PY - 2017/2/1

Y1 - 2017/2/1

N2 - 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.

AB - 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.

KW - Reshetnyak formula

KW - stability estimates

KW - tensor tomography

KW - SPACE

UR - http://www.scopus.com/inward/record.url?scp=85010664819&partnerID=8YFLogxK

U2 - 10.1088/1361-6420/33/2/025002

DO - 10.1088/1361-6420/33/2/025002

M3 - Article

AN - SCOPUS:85010664819

VL - 33

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 2

M1 - 025002

ER -

ID: 10313716