Complex Lie semigroups, Hardy spaces and the Gel'fand-Gindikin program
type: Item
instance of: scholarly article
title: Complex Lie semigroups, Hardy spaces and the Gel'fand-Gindikin program
zbMATH Open document ID: 0789.22011
DOI: 10.1016/0926-2245(91)90002-Q
published in: Differential Geometry and its Applications
publication date: 1994-01-31T00:00:00Z
review text: This paper was published originally in Russian in Vopr. Teor. Grupp Gomologicheskoj Algebry 1982, 85-98 (1982; Zbl 0581.22012). Let \(G\) be the group of motions of a bounded symmetric domain and let \(G_ \mathbb{C}\) be its complexification. It is known that there exist open subsemigroups \(\Gamma \subset G_ \mathbb{C}\) containing \(G\). These semigroups \(\Gamma\) can be viewed as noncommutative analogues of Siegel domains, where \(G \subset \Gamma\) plays the role of the skeleton. The aim of this paper is to construct analogues of Hardy spaces \(H^ 2\) on semigroups \(\Gamma\) and to study their properties.
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 43A17
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 22A20
zbMATH DE Number: 487680
zbMATH Keywords: invariant cone
zbMATH Keywords: Hermitian Lie algebra
zbMATH Keywords: complex Lie semigroup
zbMATH Keywords: pseudo- Riemannian symmetric space
zbMATH Keywords: group of motions
zbMATH Keywords: bounded symmetric domain
zbMATH Keywords: Hardy spaces
author: G. I. Olshanskii
MaRDI profile type: Publication
Wikidata QID: Q115362859
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full work available at URL: 0926-2245(91)90002-q
OpenAlex ID: W2165913551
description: scientific article; zbMATH DE number 487680