Document Type
Article
Publication Date
9-1-2003
Abstract
Let G/H be a semisimple symmetric space. Then the space L2 (G/H) can be decomposed into a finite sum of series of 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 on a bounded symmetric domain of tube type, containing G/H as a boundary component. A boundary value map is constructed and we show that it induces a G-isomorphism onto a multiplicity free subspace of full spectrum in the most continuous part Lmc2(G/H) of L2(G/H). We also relate our Hardy space to the classical Hardy space on the bounded symmetric domain.
Publication Source (Journal or Book title)
Mathematische Annalen
First Page
25
Last Page
66
Recommended Citation
Gindikin, S., Krötz, B., & Ólafsson, G. (2003). Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum. Mathematische Annalen, 327 (1), 25-66. https://doi.org/10.1007/s00208-003-0409-x