Causal compactification and Hardy spaces for spaces of Hermitian type. (Q700593)

The authors consider compactly causal symmetric spaces \(G/H\) which can be causally compactified by embedding them into the Shilov boundary of a Hermitian symmetric domain \(G_1/K_1\) of tube type. They show that these embeddings can be extended to an embedding of a natural complex domain \(\Xi\subseteq G_C/H_C\) such that the image is the complement of the zero set of a holomorphic function on \(G_1/K_1\). As a consequence they show that in these cases the Hardy spaces living on \(\Xi\) and \(G_1/K_1\), respectively, are naturally isomorphic as \(G\)-representations.