## 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.

Original language | English |
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Article number | 025002 |

Number of pages | 20 |

Journal | Inverse Problems |

Volume | 33 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Feb 2017 |

## Keywords

- Reshetnyak formula
- stability estimates
- tensor tomography
- SPACE