非紧因果对称空间的Hardy空间与最连续谱
Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum
摘要：
设$G/H$是半单对称空间.然后空间$L^2(G/H)$可以分解为由$G$的抛物子群导出的级数表示的有限和。$L^2(G/H)$光谱的最连续部分是由最小可能的抛物子群诱导的部分。在本文中，我们引入了Hardy空间规范相关的这部分的谱的一类非紧因果对称空间。Hardy空间是一个再生希尔伯特空间的全纯函数生活在一个管型有界对称区域，包含$G/H$作为一个边界组件。构造了一个边值映射，证明了它在$L^2(G/H)$的最连续部分$L_{\rm mc}^2(G/H)$中诱导$G$ -同构到全谱的一个重数自由子空间上.我们还把我们的Hardy空间与管域上的经典Hardy空间联系起来。
英文摘要：
Let $G/H$ be a semisimple symmetric space. Then the space $L^2(G/H)$ can be decomposed into a finite sum of series representations induced from parabolic subgroups of $G$. The most continuous part of the spectrum of $L^2(G/H)$ is the part induced from the smallest possible parabolic subgroup. In this paper we introduce Hardy spaces canonically related to this part of the spectrum for a class of non-compactly causal symmetric spaces. The Hardy space is a reproducing Hilbert space of holomorphic functions living on a tube type bounded symmetric domain, containing $G/H$ as a boundary component. A boundary value map is constructed and we show that it induces an $G$-isomorphism onto a multiplicity free subspace of full spectrum in the most continuous part $L_{\rm mc}^2(G/H)$ of $L^2(G/H)$. We also relate our Hardy space with the classical Hardy space on the tube domain.
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