Inverse Regge poles problem on a warped ball

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.