Abstract:
The purpose of the topic of the article in the future is to establish the equivalence in their norms of the problems of recovery the Computed Tomography and the Computational (numerical) diameter (C(N)D), which was in 2019 previously performed in the case of functions of two variables. And this was based on the equivalence of the corresponding norms proved by Frank Natterer in the same two-dimensional Sobolev spaces. In this article, for the case of functions of any dimension, a large-scale equivalence in its norm of the Radon transform and the function that generated it is established.
Keywords:
Radon transform, flexible Hilbert Sobolev space, flexible Hilbert Sobolev-Radon space, equivalence of transformations in their norms.
Citation:
N. Temirgaliyev, G. E. Taugynbayeva, A. Zh. Zhubanysheva, “Large-scale equivalence of norms of Radon transform and initial function”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 8, 87–92
\Bibitem{TemTauZhu23}
\by N.~Temirgaliyev, G.~E.~Taugynbayeva, A.~Zh.~Zhubanysheva
\paper Large-scale equivalence of norms of Radon transform and initial function
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 8
\pages 87--92
\mathnet{http://mi.mathnet.ru/ivm9912}
\crossref{https://doi.org/10.26907/0021-3446-2023-8-87-92}
Linking options:
https://www.mathnet.ru/eng/ivm9912
https://www.mathnet.ru/eng/ivm/y2023/i8/p87
This publication is cited in the following 2 articles:
Galiya Taugynbayeva, Shapen Azhgaliyev, Aksaule Zhubanysheva, Nurlan Temirgaliyev, “Full C(N)D-study of computational capabilities of Lagrange polynomials”, Mathematics and Computers in Simulation, 227 (2025), 189
N. Temirgaliev, Sh. K. Abikenova, Sh. U. Azhgaliev, E. E. Nurmoldin, G. E. Taugynbaeva, A. Zh. Zhubanysheva, “Ekvivalentnost zadach kompyuternoi tomografii c zadachami vosstanovleniya funktsii posredstvom konechnykh svertok v skheme kompyuternogo (vychislitelnogo) poperechnika”, Izv. vuzov. Matem., 2023, no. 12, 95–102
Citation in format AMSBIB
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