论文标题
Siegel上半空间上的全体形态功能的不变空间
Invariant Spaces of Holomorphic Functions on the Siegel Upper Half-Space
论文作者
论文摘要
在本文中，我们考虑组$ \ mathrm {aut} $的（射线）表示，由$ u_s（φ）f =（f \circcφ^{ - 1}）（-1}）（-1}）（Jφ^{ - 1} $ s/2} $ s/s/s/s/s $ s/s/s/s $ s/s/s $ s/s $ s/s/s $ s/s $ s/s $ s/s $ s/s $ s/s $ s/s $ s/s $表征$ \ MATHCAL U $上满足以下假设的半摩尔伯特空间$ h $ hOLMORTHIC功能：（a）$ h $非常不错； （b）$ u_s $诱导$ \ mathcal u $ in $ h $的affine Automorthisms的组$ \ mathrm {aff} $的有界射线表示。我们使用此描述来改善$ \ mathcal u $满足（a）和（b）$ \ mathrm {aff} $在$ \ mathcal u $上的半希尔伯特空间的已知表征，被$ \ m atrm {aut aut}代替。此外，我们在$ \ mathcal u $上表征了$ \ u_0 $ $ \ mathrm {aff} $下的均值全态性函数。
In this paper we consider the (ray) representations of the group $\mathrm{Aut}$ of biholomorphisms of the Siegel upper half-space $\mathcal U$ defined by $U_s(φ) f=(f\circ φ^{-1}) (J φ^{-1})^{s/2}$, $s\in\mathbb R$, and characterize the semi-Hilbert spaces $H$ of holomorphic functions on $\mathcal U$ satisfying the following assumptions: (a) $H$ is strongly decent; (b) $U_s$ induces a bounded ray representation of the group $\mathrm{Aff}$ of affine automorphisms of $\mathcal U$ in $H$. We use this description to improve the known characterization of the semi-Hilbert spaces of holomorphic functions on $\mathcal U$ satisfying (a) and (b) with $\mathrm{Aff}$ replaced by $\mathrm{Aut}$. In addition, we characterize the mean-periodic holomorphic functions on $\mathcal U$ under the representation $U_0$ of $\mathrm{Aff}$.
