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Causal compactification and Hardy spaces

Authors:	G Ó lafsson B Ø rsted

Institution:	Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803 ; Matematisk Institut, Odense Universitet, Campusvej 55, DK-5230 Odense M, Denmark

Abstract:	Let $\mathcal{M}=G/H$ be a irreducible symmetric space of Cayley type. Then $\mathcal{M}$ is diffeomorphic to an open and dense -orbit in the Shilov boundary of $G/K\times G/K$ . This compactification of $\mathcal{M}$ is causal and can be used to give answers to questions in harmonic analysis on $\mathcal{M}$ . In particular we relate the Hardy space of $\mathcal{M}$ to the classical Hardy space on the bounded symmetric domain $G/K\times G/K$ . This gives a new formula for the Cauchy-Szegö kernel for $\mathcal{M}$ .

Keywords:	Causal compactification Hardy spaces holomorphic discrete series

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