论文标题
逆向杆的逆向球问题
Inverse Regge poles problem on a warped ball
论文作者
论文摘要
在本文中，我们研究了扭曲的产品Riemannian流形的一种新型的反问题，我们将扭曲的球命名为连接边界。使用几何形状的对称性，我们首先将Regge杆的集合定义为Dirichlet到Neumann图的Meromormorphic延续的杆，相对于在变量过程的分离中出现的复杂角动量。这些gegge杆也可以看作是在变量分离后获得的一维schrödinger方程的特征值和共振集。其次，我们发现了复杂平面中雷格极点的精确渐近定位，并证明它们唯一地确定了扭曲球的翘曲功能。
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 Schrödinger 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.
