Weighted Radon Transforms of Three-Dimensional Symmetric Tensor Fields of Rank Two

Standard

Weighted Radon Transforms of Three-Dimensional Symmetric Tensor Fields of Rank Two. / Svetov, I. E.; Polyakova, A. P.

в: Siberian Advances in Mathematics, Том 36, № 1, 15.06.2026, стр. 79-92.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{c21ad671374945b6b836b084d09146d4,

title = "Weighted Radon Transforms of Three-Dimensional Symmetric Tensor Fields of Rank Two",

abstract = "Abstract: We study properties of weighted Radon transforms of symmetric-tensor fields in. We establish connections between weighted Radon transforms of-tensor fields and the Radon transform of their potentials. These connectionsdescribe the kernel and image of tomographic integral operators acting on tensor fields. Weconsider formulations of problems on reconstruction of symmetric-tensor fields from the values of the normal, longitudinal, and weighted Radontransforms and obtain inversion formulas.",

keywords = "decomposition of a tensor field, generalized Radon transform, inversion formula, tensor tomography, weighted Radon transform, тензорная томография, разложение тензорного поля, обобщенное преобразование Радона, звешенное преобразование Радона, формула обращения",

author = "Svetov, {I. E.} and Polyakova, {A. P.}",

note = "Svetov, I. E. Weighted Radon Transforms of Three-Dimensional Symmetric Tensor Fields of Rank Two / I. E. Svetov, A. P. Polyakova // Siberian Advances in Mathematics. – 2026. – Vol. 36, No. 1. – P. 79-92. – DOI 10.1134/S1055134426010086. – EDN VIAUXE. The research is supported by the Russian Science Foundation (grant no. 24-21-00200).",

year = "2026",

month = jun,

day = "15",

doi = "10.1134/S1055134426010086",

language = "English",

volume = "36",

pages = "79--92",

journal = "Siberian Advances in Mathematics",

issn = "1055-1344",

publisher = "Pleiades Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Weighted Radon Transforms of Three-Dimensional Symmetric Tensor Fields of Rank Two

AU - Svetov, I. E.

AU - Polyakova, A. P.

N1 - Svetov, I. E. Weighted Radon Transforms of Three-Dimensional Symmetric Tensor Fields of Rank Two / I. E. Svetov, A. P. Polyakova // Siberian Advances in Mathematics. – 2026. – Vol. 36, No. 1. – P. 79-92. – DOI 10.1134/S1055134426010086. – EDN VIAUXE. The research is supported by the Russian Science Foundation (grant no. 24-21-00200).

PY - 2026/6/15

Y1 - 2026/6/15

N2 - Abstract: We study properties of weighted Radon transforms of symmetric-tensor fields in. We establish connections between weighted Radon transforms of-tensor fields and the Radon transform of their potentials. These connectionsdescribe the kernel and image of tomographic integral operators acting on tensor fields. Weconsider formulations of problems on reconstruction of symmetric-tensor fields from the values of the normal, longitudinal, and weighted Radontransforms and obtain inversion formulas.

AB - Abstract: We study properties of weighted Radon transforms of symmetric-tensor fields in. We establish connections between weighted Radon transforms of-tensor fields and the Radon transform of their potentials. These connectionsdescribe the kernel and image of tomographic integral operators acting on tensor fields. Weconsider formulations of problems on reconstruction of symmetric-tensor fields from the values of the normal, longitudinal, and weighted Radontransforms and obtain inversion formulas.

KW - decomposition of a tensor field

KW - generalized Radon transform

KW - inversion formula

KW - tensor tomography

KW - weighted Radon transform

KW - тензорная томография

KW - разложение тензорного поля

KW - обобщенное преобразование Радона

KW - звешенное преобразование Радона

KW - формула обращения

UR - https://www.mendeley.com/catalogue/35a1cb84-f384-3100-bb34-1ab5cd82ba8b/

UR - https://www.scopus.com/pages/publications/105041799981

UR - https://elibrary.ru/item.asp?id=91603129

U2 - 10.1134/S1055134426010086

DO - 10.1134/S1055134426010086

M3 - Article

VL - 36

SP - 79

EP - 92

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

SN - 1055-1344

IS - 1

ER -

ID: 83369531