论文标题
球形$ p $ - adic空间和伯恩斯坦形态的Paley-Wiener定理
A Paley-Wiener theorem for spherical $p$-adic spaces and Bernstein morphisms
论文作者
论文摘要
让$ g $是（理性点）在本地非架构的$ f $上的连接还原组。在本文中，我们制定并证明了$ f $ spherical同质$ g $ -space的属性（此外，该属性还满足有限的多重属性，预计所有$ f $ f $ spherical jepherical同质$ g $ -spaces）我们称其为Paley-Wiener物业。与Delorme，Harinck和Sakellaridis的相关工作相比，这要多得多，但所包含的信息也要少得多（但是，它适用于更宽的空间）。该属性来自并行分类属性。我们还讨论了如何通过这种方法来定义伯恩斯坦的形态。
Let $G$ be (the rational points of) a connected reductive group over a local non-archimedean field $F$. In this article we formulate and prove a property of an $F$-spherical homogeneous $G$-space (which in addition satisfies the finite multiplicity property, which is expected to hold for all $F$-spherical homogeneous $G$-spaces) which we call the Paley-Wiener property. This is much more elementary, but also contains much less information, than the recent relevant work of Delorme, Harinck and Sakellaridis (however, it holds for a wider class of spaces). The property results from a parallel categorical property. We also discuss how to define Bernstein morphisms via this approach.
