TY - JOUR

T1 - THE RAY TRANSFORM OF SYMMETRIC TENSOR FIELDS WITH INCOMPLETE PROJECTION DATA ON A CONVEX NON-SMOOTH DOMAIN

AU - Вайцель, Никита Александрович

PY - 2024

Y1 - 2024

N2 - We consider the ray transform IΓ that integrates symmetric rank m tensor fields on Rn supported in a bounded convex domain D ⊂ Rn over lines. The integrals are known for the family Γ of lines l such that endpoints of the segment l ∩ D belong to a given part γ = ∂D ∩ Rn + of the boundary, for some half-space Rn + ⊂ Rn. In this work, we assume that the domain D is convex with a non-smooth boundary. In this case, we prove that the kernel of the operator IΓ coincides with the space of γ-potential tensor fields, which is a generalization of the results obtained in [2]

AB - We consider the ray transform IΓ that integrates symmetric rank m tensor fields on Rn supported in a bounded convex domain D ⊂ Rn over lines. The integrals are known for the family Γ of lines l such that endpoints of the segment l ∩ D belong to a given part γ = ∂D ∩ Rn + of the boundary, for some half-space Rn + ⊂ Rn. In this work, we assume that the domain D is convex with a non-smooth boundary. In this case, we prove that the kernel of the operator IΓ coincides with the space of γ-potential tensor fields, which is a generalization of the results obtained in [2]

KW - ray transform

KW - tensor analysis

KW - tomography with incomplete data

KW - tomography with incomplete data

KW - tensor analysis

KW - ray transform

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85212310076&origin=inward&txGid=4042b9c3c046995dc0071f23de709930

U2 - https://doi.org/10.33048/semi.2024.21.067

DO - https://doi.org/10.33048/semi.2024.21.067

M3 - Article

VL - 21

SP - 1011

EP - 1023

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

ER -