Schwartz函数的渐近性质
Asymptotics of Schwartz functions
AI总结：
本文研究分裂、单连通、几乎单代数群G的极大抛物子群P的仿射闭包X_P上的Schwartz空间，证明两种定义在经典群和G2情形下等价，并建立Poisson求和公式。
摘要：
设$G$为分裂、单连通、几乎单代数群，$P$为$G$的极大抛物子群。Braverman和Kazhdan在\cite{BKnormalized}中定义了$P^{\mathrm{der}}ackslash G$的仿射闭包$X_P$上的Schwartz空间。在若干前期工作之后，\cite{Getz:Hsu:Leslie}给出了另一种更易于分析处理的定义。当$G$为经典群或$G_2$时，我们证明这两种定义一致，并证明了Schwartz空间的一些先前猜想性质，这些性质将在应用中发挥作用。在此过程中，我们利用Fourier理论给出了$X_P$上微分算子环的另一种构造。我们还建立了这些情形下的Poisson求和公式。
英文摘要：
Let $G$ be a split, simply connected, almost simple algebraic group, and let $P$ be a maximal parabolic subgroup of $G$. Braverman and Kazhdan in \cite{BKnormalized} defined a Schwartz space on the affine closure $X_P$ of $P^{\mathrm{der}}\backslash G$. An alternate, more analytically tractable definition was given in \cite{Getz:Hsu:Leslie}, following several earlier works. When $G$ is a classical group or $G_2$, we show the two definitions coincide and prove several previously conjectured properties of the Schwartz space that will be useful in applications. Along the way, we give an alternative construction of the ring of differential operators on $X_P$ using the Fourier theory. We also establish the Poisson summation formulae in these cases.
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。
