实数、复数和四元数Grassmannian上的Radon变换
Radon transform on real, complex and quaternionic Grassmannians
摘要：
设$G_{n,k}(\bbK)$是$\bbK^n$中$k$维$\bbK$ -子空间的格拉斯曼流形，其中$\bbK=\mathbb R, \mathbb C, \mathbb H$是实数域、复数域或四元数域.对于$1\le k < k^\prime \le n-1$，我们定义Radon变换$(\mathcal R f)(η)$，$η\in G_{n,k^\prime}(\bbK)$，对于$G_{n,k}(\bbK)$上的函数$f(ξ)$，作为对所有$ξ\subset η$的积分。当$k+k^\prime \le n$时，给出了$\bbK$上正$k\times k$矩阵对称锥上Garding-Gindikin分数次积分和Cayley型微分算子的反演公式.这推广了Grinberg-Rubin最近关于真正Grassmannian的结果。
英文摘要：
Let $G_{n,k}(\bbK)$ be the Grassmannian manifold of $k$-dimensional $\bbK$-subspaces in $\bbK^n$ where $\bbK=\mathbb R, \mathbb C, \mathbb H$ is the field of real, complex or quaternionic numbers. For $1\le k < k^\prime \le n-1$ we define the Radon transform $(\mathcal R f)(η)$, $η\in G_{n,k^\prime}(\bbK)$, for functions $f(ξ)$ on $G_{n,k}(\bbK)$ as an integration over all $ξ\subset η$. When $k+k^\prime \le n$ we give an inversion formula in terms of the Gårding-Gindikin fractional integration and the Cayley type differential operator on the symmetric cone of positive $k\times k$ matrices over $\bbK$. This generalizes the recent results of Grinberg-Rubin for real Grassmannians.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
