Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets | Sciact - Система учета научной деятельности ИМ СО РАН

Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets Научная публикация

Журнал

Doklady Mathematics
ISSN: 1064-5624 , E-ISSN: 1531-8362

Вых. Данные

Год: 2024, Том: 109, Номер: 2, Страницы: 175–178 Страниц : 4 DOI: 10.1134/s1064562424702004

Ключевые слова

generalized Radon transform, integral geometry, probing, tomography, differential equation, discontinuous functions

Авторы

Anikonov D.S. ¹ , Konovalova D.S. ¹

Организации

1	Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2022-0009

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.

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

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

Поступила в редакцию:	5 февр. 2024 г.
Принята к публикации:	4 апр. 2024 г.
Опубликована в печати:	10 июн. 2024 г.
Опубликована online:	10 июн. 2024 г.

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

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