Real Harmonic Analysis on the Special Orthogonal Group
Real Harmonic Analysis on the Special Orthogonal Group
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特殊正交群的实调和分析
DOI：
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发表时间：
2018
影响因子：
1
通讯作者：
Taeyoung Lee
中科院分区：
文献类型：
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作者：
Taeyoung Lee
本文对特殊正交群上的真实的谐波分析进行了理论分析和软件实现。复值函数在特殊正交群上的非交换调和分析得到了广泛的研究。然而，人们习惯于把真实的调和分析作为复调和分析的特殊情况，并且已经有有限的结果专门针对实值函数。在这里，我们开发了一组显式公式的实值不可约酉表示的特殊正交群，并提供了几个操作性质，如导数，采样，和Clebsch-Gordon系数。此外，我们实现了复杂的和真实的谐波分析的特殊正交组到一个开源的软件包，利用并行处理，通过OpenMP库。基准研究和应用程序的球形形状匹配所示的结果的功效。
This paper presents theoretical analysis and software implementation for real harmonics analysis on the special orthogonal group. Noncommutative harmonic analysis for complex-valued functions on the special orthogonal group has been studied extensively. However, it is customary to treat real harmonic analysis as a special case of complex harmonic analysis, and there have been limited results developed specifically for real-valued functions. Here, we develop a set of explicit formulas for real-valued irreducible unitary representations on the special orthogonal group, and provide several operational properties, such as derivatives, sampling, and Clebsch-Gordon coefficients. Furthermore, we implement both of complex and real harmonics analysis on the special orthogonal group into an open source software package that utilizes parallel processing through the OpenMP library. The efficacy of the presented results are illustrated by benchmark studies and an application to spherical shape matching.