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 -