Momentum ray transforms, II: Range characterization in the Schwartz space

Momentum ray transforms, II: Range characterization in the Schwartz space Full article

Journal

Inverse Problems
ISSN: 0266-5611

Output data

Year: 2020, Volume: 36, Number: 4, Article number : 045009, Pages count : DOI: 10.1088/1361-6420/ab6a65

Tags

inverse problems; John's conditions; momentum ray transform; range characterization; ray transform; tensor analysis

Authors

Krishnan V.P. ¹ , Manna R. ¹ , Sahoo S.K. ¹ , Sharafutdinov V.A. ^2,3

Affiliations

1	TIFR Centre for Applicable Mathematics, Sharada Nagar, Chikkabommasandra, Yelahanka New Town Bangalore, India
2	Sobolev Institute of Mathematics, 4 Koptyug Avenue, Novosibirsk, 630090, Russian Federation
3	Novosibirsk State University, 2 Pirogov Street, Novosibirsk, 630090, Russian Federation

The momentum ray transform I k integrates a rank m symmetric tensor field f over lines of with the weight t k: We give the range characterization for the operator on the Schwartz space of rank m smooth fast decaying tensor fields. In dimensions, the range is characterized by certain differential equations of order which generalize the classical John equations. In the two-dimensional case, the range is characterized by certain integral conditions which generalize the classical Gelfand-Helgason-Ludwig conditions.

Krishnan V.P. , Manna R. , Sahoo S.K. , Sharafutdinov V.A.
Momentum ray transforms, II: Range characterization in the Schwartz space
Inverse Problems. 2020. V.36. N4. 045009 . DOI: 10.1088/1361-6420/ab6a65 WOS Scopus OpenAlex

Web of science:	WOS:000518972500001
Scopus:	2-s2.0-85081964028
OpenAlex:	W2973765856

DB	Citing
Scopus	20
OpenAlex	7
Web of science	20