The optimal recovery of a function from an inaccurate information on its k-plane transform

We consider the optimal recovery of the βth degree of the Laplacian value on a function from the information on its κ-plane transform, measured with an error. We present the error of the optimal recovery and the set of optimal methods on classes with the bounded ath degree of the Laplacian, where 0 ≤ β < α. As a consequence, we give one inequality for the norms of the degree of the Laplace operator and the κ-plane transform. Particular cases include new inversion methods and inequalities for the classical Radon and x-ray transforms. © 2016 IOP Publishing Ltd Printed in the UK.

Авторы
Редакторы
-
Журнал
Издательство
Institute of Physics Publishing
Номер выпуска
6
Язык
Английский
Страницы
-
Статус
Опубликовано
Подразделение
-
Номер
065004
Том
32
Год
2016
Организации
  • 1 Peoples' Friendship University of Russia, Miklukho-Maklaya ul., 6, Moscow, Russian Federation
Ключевые слова
approximations; extremal problems; Laplace operator; optimal recovery; Radon transform; x-ray transform; κ-plane transform
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/3955/