On Spectral Representations of Tensor Random Fields on the Sphere
On Spectral Representations of Tensor Random Fields on the Sphere
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球面上张量随机场的谱表示
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
L. Sakhno
中科院分区：
文献类型：
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作者：
N. Leonenko;L. Sakhno
本文在旋转群表示理论的基础上，研究了球面上张量随机场的表示。引入张量场的特殊分量，并施加弱各向同性和均方连续的条件，导出了它们的广义球函数谱分解。给出了分解的随机系数的性质，包括高斯性条件等重要问题。
We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square continuity, we derive their spectral decompositions in terms of generalized spherical functions. The properties of random coefficients of the decompositions are characterized, including such an important question as conditions of Gaussianity.