Large-Scale Equivalence of Norms of the Radon Transform and Initial Function

Temirgaliyev N. Taugynbayeva G.E. Zhubanysheva A.Z.
August 2023 Pleiades Publishing

Russian Mathematics
2023 #67 Issue 8 62 - 66 pp.

Abstract: This study aims to establish equivalences (in norm) of the problems of reconstructing computed tomography and computational (numerical) diameter (C(N)D), which was done in 2019 for functions of two variables. This was based on the equivalence of respective norms in the same two-dimensional Sobolev spaces proved by Frank Natterer. In this study, we prove the equivalence (in norm) of the Radon transform and the function that generated it for the case of functions of any dimension with large-scale prospects for application.

equivalence of transforms in norm , flexible Hilbert Sobolev space , flexible Hilbert Sobolev–Radon space , Radon transform

Text of the article Перейти на текст статьи

Institute of Theoretical Mathematics and Scientific Computations, Gumilev Eurasian National University, Astana, 010008, Kazakhstan

Institute of Theoretical Mathematics and Scientific Computations

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026