论文标题
gl（n）的某些L^2-Norm和Whittaker功能的渐近界
Certain L^2-norm and Asymptotic bounds of Whittaker Function for GL(n)
论文作者
论文摘要
$ gl（N，\ Mathbb R）$的Whittaker功能以其在尖端形式的傅立叶范围扩展中而闻名。他们在Siegel套装中的行为很广泛。在本文中，我们将Whittaker功能的一些潜在有用的属性插入了组$ gl（n，\ mathbb r）$和mirobolic $ p_n $。我们证明了惠特克在某些措施方面起作用的正方形整合，从而扩展了Jacquet和Shalika的定理。对于主要系列表示，我们在整个组$ gl（n，\ mathbb r）$上给出了平滑惠特克功能的各种渐近界。由于缺乏良好的术语，我们使用Whittaker功能来指惠特克模型中的$ k $ finite或光滑向量。
Whittaker functions of $GL(n, \mathbb R)$ , are most known for its role in the Fourier-Whittaker expansion of cusp forms. Their behavior in the Siegel set, in large, is well-understood. In this paper, we insert into the literature some potentially useful properties of Whittaker function over the group $GL(n, \mathbb R)$ and the mirobolic group $P_n$. We proved the square integrabilty of the Whittaker functions with respect to certain measures, extending a theorem of Jacquet and Shalika . For principal series representations, we gave various asymptotic bounds of smooth Whittaker functions over the whole group $GL(n, \mathbb R)$. Due to the lack of good terminology, we use whittaker functions to refer to $K$-finite or smooth vectors in the Whittaker model.
