Inverse Regge poles problem on a warped ball

IF 1.2 4区数学 Q2 MATHEMATICS, APPLIED

Inverse Problems and Imaging Pub Date : 2022-03-25 DOI:10.3934/ipi.2023031

Jack Borthwick, N. Boussaid, Thierry Daud'e

引用次数: 1

Abstract

In this paper, we study a new type of inverse problem on warped product Riemannian manifolds with connected boundary that we name warped balls. Using the symmetry of the geometry, we first define the set of Regge poles as the poles of the meromorphic continuation of the Dirichlet-to-Neumann map with respect to the complex angular momentum appearing in the separation of variables procedure. These Regge poles can also be viewed as the set of eigenvalues and resonances of a one-dimensional Schr\"odinger equation on the half-line, obtained after separation of variables. Secondly, we find a precise asymptotic localisation of the Regge poles in the complex plane and prove that they uniquely determine the warping function of the warped balls.

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弯曲球上的逆雷格极问题

本文研究了具有连通边界的翘曲积黎曼流形上的一类新的反问题，称之为翘曲球。利用几何的对称性，我们首先将Regge极点集定义为Dirichlet到Neumann映射关于变量分离过程中出现的复角动量的亚纯延拓的极点。这些Regge极点也可以看作是分离变量后得到的半线上一维Schr“odinger方程的特征值和共振的集合。其次，我们发现了Regge极点在复平面上的精确渐近局部化，并证明了它们唯一地确定了翘曲球的翘曲函数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Inverse Problems and Imaging 数学-物理：数学物理

CiteScore

2.50

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Inverse Problems and Imaging publishes research articles of the highest quality that employ innovative mathematical and modeling techniques to study inverse and imaging problems arising in engineering and other sciences. Every published paper has a strong mathematical orientation employing methods from such areas as control theory, discrete mathematics, differential geometry, harmonic analysis, functional analysis, integral geometry, mathematical physics, numerical analysis, optimization, partial differential equations, and stochastic and statistical methods. The field of applications includes medical and other imaging, nondestructive testing, geophysical prospection and remote sensing as well as image analysis and image processing. This journal is committed to recording important new results in its field and will maintain the highest standards of innovation and quality. To be published in this journal, a paper must be correct, novel, nontrivial and of interest to a substantial number of researchers and readers.