X-ray transform on Sobolev spaces › Обзор исследований

Standard

X-ray transform on Sobolev spaces. / Sharafutdinov, Vladimir A.

в: Inverse Problems, Том 37, № 1, 015007, 01.2021.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Sharafutdinov, VA 2021, 'X-ray transform on Sobolev spaces', Inverse Problems, Том. 37, № 1, 015007. https://doi.org/10.1088/1361-6420/abb5e0

APA

Sharafutdinov, V. A. (2021). X-ray transform on Sobolev spaces. Inverse Problems, 37(1), [015007]. https://doi.org/10.1088/1361-6420/abb5e0

Vancouver

Sharafutdinov VA. X-ray transform on Sobolev spaces. Inverse Problems. 2021 янв.;37(1):015007. doi: 10.1088/1361-6420/abb5e0

Author

Sharafutdinov, Vladimir A. / X-ray transform on Sobolev spaces. в: Inverse Problems. 2021 ; Том 37, № 1.

BibTeX

@article{c7c68e37328b4087808779d5ee6cc970,

title = "X-ray transform on Sobolev spaces",

abstract = "The x-ray transform I integrates a function fon 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.",

keywords = "x-ray transform, Sobolev spaces, John equations, Reshetnyak formula",

author = "Sharafutdinov, {Vladimir A.}",

year = "2021",

month = jan,

doi = "10.1088/1361-6420/abb5e0",

language = "English",

volume = "37",

journal = "Inverse Problems",

issn = "0266-5611",

publisher = "IOP Publishing Ltd.",

number = "1",

}

RIS

TY - JOUR

T1 - X-ray transform on Sobolev spaces

AU - Sharafutdinov, Vladimir A.

PY - 2021/1

Y1 - 2021/1

N2 - The x-ray transform I integrates a function fon 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.

AB - The x-ray transform I integrates a function fon 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.

KW - x-ray transform

KW - Sobolev spaces

KW - John equations

KW - Reshetnyak formula

UR - http://www.scopus.com/inward/record.url?scp=85098241509&partnerID=8YFLogxK

U2 - 10.1088/1361-6420/abb5e0

DO - 10.1088/1361-6420/abb5e0

M3 - Article

AN - SCOPUS:85098241509

VL - 37

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 1

M1 - 015007

ER -

ID: 27374173