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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Causal compactification and Hardy spaces


Authors: G. Ólafsson and B. Ørsted
Journal: Trans. Amer. Math. Soc. 351 (1999), 3771-3792
MSC (1991): Primary 43A85, 22E46; Secondary 43A65, 53C35
Published electronically: March 1, 1999
MathSciNet review: 1458309
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\mathcal{M}=G/H$ be a irreducible symmetric space of Cayley type. Then $\mathcal{M}$ is diffeomorphic to an open and dense $G$-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 $\mathcal{M}$.


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Additional Information

G. Ólafsson
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: olafsson@math.lsu.edu

B. Ørsted
Affiliation: Matematisk Institut, Odense Universitet, Campusvej 55, DK-5230 Odense M, Denmark
Email: orsted@imada.ou.dk

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02101-7
PII: S 0002-9947(99)02101-7
Keywords: Causal compactification, Hardy spaces, holomorphic discrete series
Received by editor(s): April 29, 1996
Received by editor(s) in revised form: March 10, 1997
Published electronically: March 1, 1999
Additional Notes: The first named author was supported by NSF grant DMS-9626541, LEQSF grant (1996-99)-RD-A-12 and the Danish Research Council
Article copyright: © Copyright 1999 American Mathematical Society