Hardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum

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dc.creatorGindikin, Simon
dc.creatorKroetz, Bernhard
dc.creatorOlafsson, Gestur
dc.date2001-11-14
dc.date2002-10-30
dc.date.accessioned2026-07-07T04:44:36Z
dc.date.available2026-07-07T04:44:36Z
dc.descriptionLet $G/H$ 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.
dc.descriptionRevised version: readability improved, minor errors corrected. To appear in Math. Annalen, 36 pages
dc.identifierhttps://arxiv.org/abs/math/0111172
dc.identifierhttp://arxiv.org/abs/math/0111172
dc.identifierMath. Ann. 327(1) (2003), 25-66
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62655
dc.subjectRepresentation Theory
dc.subjectComplex Variables
dc.subject22E30, 32M15, 43A85
dc.titleHardy spaces for non-compactly causal symmetric spaces and the most continuous spectrum
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