Fourier，Gauss，Fraunhofer，Porod与矩量形状问题
Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem
摘要：
我们展示了如何傅立叶变换的形状在任何数量的维度可以简化使用高斯定律和明确评估多边形在二维，多面体三维等，我们还展示了如何结合傅立叶和高斯可以涉及到许多经典的物理和数学问题。例子包括夫琅禾费衍射图案，Porods定律，Hopfs Umlauffe，等周不等式和Didos问题。我们还使用这种方法来提供一个替代的衍生戴维斯的Motzkin-勋伯格公式的多边形在复杂的平面上的扩展。
英文摘要：
We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gauss can be related to numerous classical problems in physics and mathematics. Examples include Fraunhofer diffraction patterns, Porods law, Hopfs Umlaufsatz, the isoperimetric inequality and Didos problem. We also use this approach to provide an alternative derivation of Davis's extension of the Motzkin-Schoenberg formula to polygons in the complex plane.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
