Stiefel流形和Grassmann流形上的$λ$ -余弦变换、微分算子和Funk变换
The $λ$-Cosine Transforms, Differential Operators, and Funk Transforms on Stiefel and Grassmann Manifolds
摘要：
在Stiefel流形和Grassmann流形上引入了一类新的与$λ$ -余弦变换和Funk-Radon变换相关的不变微分算子.这些算子降低了$λ$ -余弦变换的阶数，并产生新的反演公式。研究了低秩矩阵积分所对应的中间Funk余弦变换。主要工具是矩阵空间上的极式分解和傅里叶分析。
英文摘要：
We introduce a new family of invariant differential operators associated with $λ$-cosine and Funk-Radon transforms on Stiefel and Grassmann manifolds. These operators reduce the order of the $λ$-cosine transforms and yield new inversion formulas. Intermediate Funk-cosine transforms corresponding to integration over matrices of lower rank are studied. The main tools are polar decomposition and Fourier analysis on matrix space.
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