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.

中文翻译：

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Stiefel 和 Grassmann 流形上的 λ-余弦变换、微分算子和 Funk 变换

我们引入了一系列与 Stiefel 和 Grassmann 流形上的λ -余弦和 Funk-Radon 变换相关的新的不变微分算子。这些算子降低了λ -余弦变换的阶数并产生新的反演公式。研究了对应于低秩矩阵上的积分的中间 Funk-cosine 变换。主要工具是矩阵空间的极坐标分解和傅立叶分析。