Abstract: Some questions concerning the inversion of the classical and generalized integral Radon transforms are discussed. The main issue is to determine information about the integrand if the values of some integrals are known. A feature of this work is that a function is integrated over hyperplanes in a finite-dimensional Euclidean space and the integrands depend not only on the variables of integration, but also on some of the variables characterizing the hyperplanes. The independent variables describing the known integrals are fewer than those in the unknown integrand. We consider discontinuous integrands defined on specifically introduced pseudoconvex sets. A Stefan-type problem of finding discontinuity surfaces of the integrand is posed. Formulas for solving the problem under study are derived by applying special integro-differential operators to known data.

Cite: Anikonov D.S. , Konovalova D.S.
Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets
Doklady Mathematics. 2024. V.109. N2. P.175–178. DOI: 10.1134/s1064562424702004 WOS Scopus РИНЦ OpenAlex

Original: Аниконов Д.С. , Коновалова Д.С.
Проблема обращения преобразований Радона, определенных на псевдовыпуклых множествах
Доклады Академии наук. Серия: Математика, информатика, процессы управления. 2024. Т.516. №1. С.93-97. DOI: 10.31857/S2686954324020151 РИНЦ OpenAlex

Dates:

Submitted:	Feb 5, 2024
Accepted:	Apr 4, 2024
Published print:	Jun 10, 2024
Published online:	Jun 10, 2024

Identifiers:

Web of science:	WOS:001242673900005
Scopus:	2-s2.0-85195572686
Elibrary:	68225995
OpenAlex:	W4399511311

Citing: Пока нет цитирований

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