TY - JOUR

T1 - On a Generalization of Exponential Ray Transform in Tomography

AU - Derevtsov, E. Yu

N1 - Publisher Copyright: © 2021, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/3

Y1 - 2021/3

N2 - We consider the operator of generalized exponential ray transform whose values are the initial data in the emission computer tomography problem. We establish connections between exponential ray transforms of different orders and obtain the differential equations satisfied by the exponential ray transforms. We prove the uniqueness theorems for boundary value and initial-boundary value problems for the corresponding equations We also discuss close connections of generalized exponential ray transforms with integral geometry of tensor fields and tomography problems.

AB - We consider the operator of generalized exponential ray transform whose values are the initial data in the emission computer tomography problem. We establish connections between exponential ray transforms of different orders and obtain the differential equations satisfied by the exponential ray transforms. We prove the uniqueness theorems for boundary value and initial-boundary value problems for the corresponding equations We also discuss close connections of generalized exponential ray transforms with integral geometry of tensor fields and tomography problems.

UR - http://www.scopus.com/inward/record.url?scp=85100607927&partnerID=8YFLogxK

U2 - 10.1007/s10958-021-05235-3

DO - 10.1007/s10958-021-05235-3

M3 - Article

AN - SCOPUS:85100607927

VL - 253

SP - 369

EP - 381

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 3

ER -