论文标题
Riesz运算符和双曲线组的一些球形表示
Riesz operators and some spherical representations for hyperbolic groups
论文作者
论文摘要
我们在Gromov双曲线组的背景下介绍了Riesz运算符，以研究双曲线基团的非单一边界的一个参数家族。我们证明了渐近Schur的关系，后者是本文的主要结果。达到归一化，Riesz运营商在knapp-stein Intertwiner的双曲线群的背景下扮演着角色，用于LIE组的互补系列。假设Riesz运营商的积极性，我们为双曲线组定义了互补序列的类似物，并证明了它们的不可约性。
We introduce the Riesz operator in the context of Gromov hyperbolic groups in order to investigate a one parameter family of non unitary boundary Hilbertian representations of hyperbolic groups. We prove asymptotic Schur's relations, the latter being the main result of this paper. Up to normalization, the Riesz operator plays the role in the context of hyperbolic groups of the Knapp-Stein intertwiner for complementary series for Lie groups. Assuming the positivity of the Riesz operator, we define an analogue of complementary series for hyperbolic groups and prove their irreducibility.
