Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803 ; Matematisk Institut, Odense Universitet, Campusvej 55, DK-5230 Odense M, Denmark
Abstract:
Let be a irreducible symmetric space of Cayley type. Then is diffeomorphic to an open and dense -orbit in the Shilov boundary of . This compactification of is causal and can be used to give answers to questions in harmonic analysis on . In particular we relate the Hardy space of to the classical Hardy space on the bounded symmetric domain . This gives a new formula for the Cauchy-Szegö kernel for .