Causal compactification and hardy spaces
Let M = G/H be a irreducible symmetric space of Cayley type. Then M is diffeomorphic to an open and dense G-orbit in the Shilov boundary of G/K x G/K. This compactification of M is causal and can be used to give answers to questions in harmonic analysis on M. In particular we relate the Hardy space of M to the classical Hardy space on the bounded symmetric domain G/K x G/K. This gives a new formula for the Cauchy-Szegö kernel for M. ©1999 American Mathematical Society.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
Ólafsson, G., & Ørsted, B. (1999). Causal compactification and hardy spaces. Transactions of the American Mathematical Society, 351 (9), 3771-3792. https://doi.org/10.1090/s0002-9947-99-02101-7