The John equation for tensor tomography in three-dimensions

John proved that a function $j$ on the manifold of lines in $R^3$ belongs to therange of the x-ray transform if and only if $j$ satisfies some second orderdifferential equation and obeys some smoothness and decay conditions. Wegeneralize the John equation to the case of the x-ray transform on arbitr...

Full description

Saved in:
Bibliographic Details
Published in:Inverse problems 2016-10, Vol.32 (10), p.105013
Main Authors: Nadirashvili, Nikolai S, Sharafutdinov, Vladimir A, Vlăduţ, Serge G
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:John proved that a function $j$ on the manifold of lines in $R^3$ belongs to therange of the x-ray transform if and only if $j$ satisfies some second orderdifferential equation and obeys some smoothness and decay conditions. Wegeneralize the John equation to the case of the x-ray transform on arbitraryrank symmetric tensor fields: a function j on the manifold of lines in$R^3$belongs to the range of the x-ray transform on rank m symmetric tensor fieldsif and only if $j$ satisfies some differential equation of order 2(m + 1) andobeys some smoothness and decay conditions.
ISSN:0266-5611
1361-6420
DOI:10.1088/0266-5611/32/10/105013