球面上的自旋波
Spin Wavelets on the Sphere
摘要：
近年来，一个快速增长的文献已经集中在小波系统的构造来分析定义在球面上的函数。我们在本文中的目的是推广这些建设的情况下，部分的线丛，而不是普通的标量值函数，被认为是。特别是，我们提出了{ \em针型自旋小波}作为最近推出的Narcowich，Petrushev和沃德，然后考虑更一般的流形盖勒和Mayeli针方法的扩展。我们讨论了实域和调和域中的局部化性质，并研究了自旋随机场分析的随机性质。我们的研究结果是强烈的宇宙学应用的动机，特别是在宇宙微波背景偏振数据的分析。
英文摘要：
In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of line bundles, rather than ordinary scalar-valued functions, are considered. In particular, we propose {\em needlet-type spin wavelets} as an extension of the needlet approach recently introduced by Narcowich, Petrushev and Ward, and then considered for more general manifolds by Geller and Mayeli. We discuss localization properties in the real and harmonic domains, and investigate stochastic properties for the analysis of spin random fields. Our results are strongly motivated by cosmological applications, in particular in connection to the analysis of Cosmic Microwave Background polarization data.
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