X-ray transform on Sobolev spaces | Sciact

X-ray transform on Sobolev spaces Full article

Journal

Inverse Problems
ISSN: 0266-5611

Output data

Year: 2021, Volume: 37, Number: 1, Article number : 015007, Pages count : DOI: 10.1088/1361-6420/abb5e0

Authors

Sharafutdinov V.A. ^1,2

Affiliations

1	Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, 2 Pirogov Street, Novosibirsk, 630090, Russian Federation

The x-ray transform I integrates a function f on over lines. The range characterization of the x-ray transform on the Schwartz space is well known, the main ingredient of the characterization is some system of second order differential equations that are called John's equations. The Reshetnyak formula equates the norm to some special norm of If, it was also known before. We prove a new version of the Reshetnyak formula that involves first order derivatives of If with respect to the ξ-variable. On using the latter formula, we obtain the range characterization of the x-ray transform on Sobolev spaces.

Sharafutdinov V.A.
X-ray transform on Sobolev spaces
Inverse Problems. 2021. V.37. N1. 015007 . DOI: 10.1088/1361-6420/abb5e0 WOS Scopus OpenAlex

Web of science:	WOS:000599803600001
Scopus:	2-s2.0-85098241509
OpenAlex:	W3084300587

DB	Citing
Scopus	5
OpenAlex	4
Web of science	2