论文标题
指纹，lessist和二次差异
Fingerprints, lemniscates and quadratic differentials
论文作者
论文摘要
我们通过约旦曲线的指纹讨论对二维形状识别理论的某些方面。 P.〜ebenfelt，D.〜Khavinson和H.〜Shapiro提出的一种有趣的问题的方法，并由M.〜 Younsi进一步扩展，揭示了一个事实，即多项式诱导的指纹可以作为某些功能公式的产品作为解决方案的解决方案，更普遍地将其用于解决方案。 我们的主要目的是开发一种方法，该方法将约旦曲线的指纹与某些二次差速器的轨迹和正交轨迹组成的弧形组成，并与涉及适当的Riemann映射功能下的这些Quadratic差速器的功能方程式的解决方案。特别是，我们表明，P.〜ebenfelt，D.〜Khavinson和H.〜Shapiro的先前结果以及M.〜Younsi的最新结果来自我们更一般的定理作为特殊情况。
We discuss some aspects of the theory of recognition of two-dimensional shapes by means of fingerprints of Jordan curves. An interesting approach to problems on shape recognition suggested by P.~Ebenfelt, D.~Khavinson, and H.~Shapiro and extended further by M.~Younsi reveals the fact that the fingerprints of polynomial lemniscates and, more generally, fingerprints of rational lemniscates can be obtained as solutions to certain functional equations involving Blaschke products. Our main goal here is to develop an approach which relates fingerprints of Jordan curves composed of arcs of trajectories and orthogonal trajectories of certain quadratic differentials with solutions of functional equations involving pullbacks of these quadratic differentials under appropriate Riemann mapping functions. In particular, we show that the previous results of P.~Ebenfelt, D.~Khavinson, and H.~Shapiro and the recent results of M.~Younsi follow from our more general theorems as special cases.
