论文标题
高级司法的Quasianticitity，不确定性和整体转换
Quasianalyticity, uncertainty, and integral transforms on higher grassmannians
论文作者
论文摘要
我们调查了分销$ f $对真正的Grassmannian $ \ Mathrm {gr} _K（\ Mathbb r^n）$的支持，其频谱（即其非平凡$ \ MATHRM O（N）$ - 组件，仅限于所有$ \ Mathrm O（n）$ o（n）$（N）$（n）$ o（n）$ o（n）$（n）$（n）$（n）$ - n）$（n）$（n）$ - n）。我们证明，除非$λ$是共同的，否则在某个时候不能支持$ f $。我们利用这种不确定性原则来证明，如果$ 2 \ leq k \ leq n-2 $，那么在任何单个开放的schubert cell $σ^k $中都无法支持格拉斯曼尼亚分布的余弦变换。对于某些更通用的$α$ - cosine变换和稻米之间的ra thrunctions也是如此，更一般而言，对于各种$ \ mathrm {gl} _n（\ Mathbb r）$ - 模块。然后将这些结果应用于凸几何和几何层析成像，其中获得了Aleksandrov投影定理，Funk section定理以及Klain's和Schneider的Indentivity定理，以获得凸价值。
We investigate the support of a distribution $f$ on the real grassmannian $\mathrm{Gr}_k(\mathbb R^n)$ whose spectrum, namely its nontrivial $\mathrm O(n)$-components, is restricted to a subset $Λ$ of all $\mathrm O(n)$-types. We prove that unless $Λ$ is co-sparse, $f$ cannot be supported at a point. We utilize this uncertainty principle to prove that if $2\leq k\leq n-2$, then the cosine transform of a distribution on the grassmannian cannot be supported inside any single open Schubert cell $Σ^k$. The same holds for certain more general $α$-cosine transforms and for the Radon transform between grassmannians, and more generally for various $\mathrm{GL}_n(\mathbb R)$-modules. These results are then applied to convex geometry and geometric tomography, where sharper versions of the Aleksandrov projection theorem, Funk section theorem, and Klain's and Schneider's injectivity theorems for convex valuations are obtained.
