Stability estimates for the X-ray transform on simple asymptotically hyperbolic manifolds

Nikolas Eptaminitakis

doi:10.48550/arXiv.2104.01674

Stability estimates for the X-ray transform on simple asymptotically hyperbolic manifolds

Nikolas Eptaminitakis^*

^*Corresponding author for this work

Institute of Differential Geometry

Research output: Contribution to journal › Article › Research › peer review

Abstract

We study the normal operator to the geodesic X-ray transform on functions in the setting of simple asymptotically hyperbolic manifolds. We construct a parametrix for the normal operator in the 0-pseudodifferential calculus and use it to show a stability estimate.

Original language	English
Pages (from-to)	487-516
Number of pages	30
Journal	Pure and Applied Analysis
Volume	4
Issue number	3
E-pub ahead of print	4 Dec 2022
DOIs	https://doi.org/10.48550/arXiv.2104.01674 https://doi.org/10.2140/paa.2022.4.487
Publication status	Published - 2022

Keywords

0-calculus
asymptotically hyperbolic manifolds
normal operator
stability
X-ray transform

ASJC Scopus subject areas

Analysis
Mathematical Physics

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title = "Stability estimates for the X-ray transform on simple asymptotically hyperbolic manifolds",

abstract = "We study the normal operator to the geodesic X-ray transform on functions in the setting of simple asymptotically hyperbolic manifolds. We construct a parametrix for the normal operator in the 0-pseudodifferential calculus and use it to show a stability estimate.",

keywords = "0-calculus, asymptotically hyperbolic manifolds, normal operator, stability, X-ray transform",

author = "Nikolas Eptaminitakis",

note = "Publisher Copyright: {\textcopyright} 2022 Mathematical Sciences Publishers.",

year = "2022",

doi = "10.48550/arXiv.2104.01674",

language = "English",

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T1 - Stability estimates for the X-ray transform on simple asymptotically hyperbolic manifolds

AU - Eptaminitakis, Nikolas

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AB - We study the normal operator to the geodesic X-ray transform on functions in the setting of simple asymptotically hyperbolic manifolds. We construct a parametrix for the normal operator in the 0-pseudodifferential calculus and use it to show a stability estimate.

KW - 0-calculus

KW - asymptotically hyperbolic manifolds

KW - normal operator

KW - stability

KW - X-ray transform

UR - https://www.scopus.com/pages/publications/85180802109

U2 - 10.48550/arXiv.2104.01674

DO - 10.48550/arXiv.2104.01674

M3 - Article

SN - 2578-5885

VL - 4

SP - 487

EP - 516

JO - Pure and Applied Analysis

JF - Pure and Applied Analysis

IS - 3

ER -

Stability estimates for the X-ray transform on simple asymptotically hyperbolic manifolds

Abstract

Keywords

ASJC Scopus subject areas

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