Complex Lie semigroups, Hardy spaces and the Gel'fand-Gindikin program
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.
scientific article; zbMATH DE number 487680