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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. p. 111-117.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

Harvard

Derevtsov, E, Volkov, Y & Schuster, T 2020, Integral operators at settings and investigations of tensor tomography problems. in Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy: A Liber Amicorum to Professor Godunov. Springer International Publishing AG, pp. 111-117. https://doi.org/10.1007/978-3-030-38870-6_15

APA

Derevtsov, E., Volkov, Y., & Schuster, T. (2020). Integral operators at settings and investigations of tensor tomography problems. In Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy: A Liber Amicorum to Professor Godunov (pp. 111-117). Springer International Publishing AG. https://doi.org/10.1007/978-3-030-38870-6_15

Vancouver

Derevtsov E, Volkov Y, Schuster T. Integral operators at settings and investigations of tensor tomography problems. In Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy: A Liber Amicorum to Professor Godunov. Springer International Publishing AG. 2020. p. 111-117 doi: 10.1007/978-3-030-38870-6_15

Author

Derevtsov, Evgeny ; Volkov, Yuriy ; Schuster, Thomas. / Integral operators at settings and investigations of tensor tomography problems. Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy: A Liber Amicorum to Professor Godunov. Springer International Publishing AG, 2020. pp. 111-117

BibTeX

@inbook{731a34586027405ca7eded354dc3d528,
title = "Integral operators at settings and investigations of tensor tomography problems",
abstract = "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.",
author = "Evgeny Derevtsov and Yuriy Volkov and Thomas Schuster",
note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2020.",
year = "2020",
month = apr,
day = "3",
doi = "10.1007/978-3-030-38870-6_15",
language = "English",
isbn = "9783030388690",
pages = "111--117",
booktitle = "Continuum Mechanics, Applied Mathematics and Scientific Computing",
publisher = "Springer International Publishing AG",
address = "Switzerland",

}

RIS

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