具有可逆射线变换的流形上大固定频率的各向异性卡尔德龙问题

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-10-05 DOI:10.1112/jlms.13006

Shiqi Ma, Suman Kumar Sahoo, Mikko Salo

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引用次数: 0

摘要

我们考虑了在某些黎曼流形上以较大固定频率从狄利克特到诺依曼映射恢复势的逆问题。我们将 Uhlmann 和 Wang [arXiv:2104.03477] 的早期结果扩展到简单流形的情况，并更广泛地扩展到大地射线变换稳定可逆的流形。这一论证涉及高斯光束准模态的不变式构造，其基本常数具有均匀的约束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform

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The anisotropic Calderón problem at large fixed frequency on manifolds with invertible ray transform

We consider the inverse problem of recovering a potential from the Dirichlet to Neumann map at a large fixed frequency on certain Riemannian manifolds. We extend the earlier result of Uhlmann and Wang [arXiv:2104.03477] to the case of simple manifolds, and more generally to manifolds where the geodesic ray transform is stably invertible. The argument involves an invariantly formulated construction of Gaussian beam quasimodes with uniform bounds for the underlying constants.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.