The Reshetnyak formula and Natterer stability estimates in tensor tomography

Результат исследования: Научные публикации в периодических изданияхстатья

4 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Номер статьи025002
Число страниц20
ЖурналInverse Problems
Том33
Номер выпуска2
DOI
СостояниеОпубликовано - 1 фев 2017

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