Radon变换和初始函数范数的大尺度等价

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2023-11-20 DOI:10.3103/s1066369x23080091

N. Temirgaliyev, G. E. Taugynbayeva, A. Zh. Zhubanysheva

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引用次数: 0

摘要

摘要本研究旨在建立计算机断层重建问题与计算(数值)直径(C(N)D)的等价(范数)，该问题于2019年针对两个变量的函数完成。这是基于Frank Natterer证明的相同二维Sobolev空间中各自范数的等价性。本文在具有大规模应用前景的任意维函数的情况下，证明了Radon变换及其生成函数的等价性(范数上)。

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

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.

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.