Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная › Рецензирование
Integral operators at settings and investigations of tensor tomography problems. / Derevtsov, Evgeny; Volkov, Yuriy; Schuster, Thomas.
Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy: A Liber Amicorum to Professor Godunov. Springer International Publishing AG, 2020. стр. 111-117.Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › глава/раздел › научная › Рецензирование
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TY - CHAP
T1 - Integral operators at settings and investigations of tensor tomography problems
AU - Derevtsov, Evgeny
AU - Volkov, Yuriy
AU - Schuster, Thomas
N1 - Publisher Copyright: © Springer Nature Switzerland AG 2020.
PY - 2020/4/3
Y1 - 2020/4/3
N2 - Generalizations of attenuated ray transform (ART) and back-projection operators of tomography are suggested. The operators of ART of order m contain a complex-valued absorption, the weights of more general form, and the internal sources depending on time. Connections between ART of various orders are established, and corresponding differential equations and uniqueness theorems are obtained. We define the angular moments of ART of order m, representing generalization of back-projection operator, and establish connections between the moments of different orders. The generalized ART and angular moment operators have applications in integral geometry and tomography.
AB - Generalizations of attenuated ray transform (ART) and back-projection operators of tomography are suggested. The operators of ART of order m contain a complex-valued absorption, the weights of more general form, and the internal sources depending on time. Connections between ART of various orders are established, and corresponding differential equations and uniqueness theorems are obtained. We define the angular moments of ART of order m, representing generalization of back-projection operator, and establish connections between the moments of different orders. The generalized ART and angular moment operators have applications in integral geometry and tomography.
UR - http://www.scopus.com/inward/record.url?scp=85087705933&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-38870-6_15
DO - 10.1007/978-3-030-38870-6_15
M3 - Chapter
AN - SCOPUS:85087705933
SN - 9783030388690
SP - 111
EP - 117
BT - Continuum Mechanics, Applied Mathematics and Scientific Computing
PB - Springer International Publishing AG
ER -
ID: 34192886