Complex Lie semigroups, Hardy spaces and the Gel’fand-Gindikin program. (English) Zbl 0789.22011

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.


22E15 General properties and structure of real Lie groups
43A17 Analysis on ordered groups, \(H^p\)-theory
22E30 Analysis on real and complex Lie groups
22A20 Analysis on topological semigroups


Zbl 0581.22012
Full Text: DOI


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