A1 Journal article (refereed)
Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds (2022)
Krupchyk, K., Liimatainen, T., & Salo, M. (2022). Linearized Calderón problem and exponentially accurate quasimodes for analytic manifolds. Advances in Mathematics, 403, Article 108362. https://doi.org/10.1016/j.aim.2022.108362
JYU authors or editors
Publication details
All authors or editors: Krupchyk, Katya; Liimatainen, Tony; Salo, Mikko
Journal or series: Advances in Mathematics
ISSN: 0001-8708
eISSN: 1090-2082
Publication year: 2022
Publication date: 05/04/2022
Volume: 403
Article number: 108362
Publisher: Elsevier Inc.
Publication country: United States
Publication language: English
DOI: https://doi.org/10.1016/j.aim.2022.108362
Publication open access: Openly available
Publication channel open access: Partially open access channel
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/82386
Web address of parallel published publication (pre-print): https://arxiv.org/abs/2009.05699
Abstract
In this article we study the linearized anisotropic Calderón problem on a compact Riemannian manifold with boundary. This problem amounts to showing that products of pairs of harmonic functions of the manifold form a complete set. We assume that the manifold is transversally anisotropic and that the transversal manifold is real analytic and satisfies a geometric condition related to the geometry of pairs of intersecting geodesics. In this case, we solve the linearized anisotropic Calderón problem. The geometric condition does not involve the injectivity of the geodesic X-ray transform. Crucial ingredients in the proof of our result are the construction of Gaussian beam quasimodes on the transversal manifold, with exponentially small errors, as well as the FBI transform characterization of the analytic wave front set.
Keywords: inverse problems; partial differential equations; Riemannian manifolds
Free keywords: inverse problems; Riemannian manifold; conformally transversally anisotropic; Gaussian quasimodes; WKB construction; wave front set
Contributing organizations
Ministry reporting: Yes
Reporting Year: 2022
JUFO rating: 3
