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Causal
compactification and Hardy Spaces for spaces of Hermitian
type
Frank Betten and Gestur Ólafsson |
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Vol. 200 (2001), No. 2, 273–312
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Abstract |
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Let G∕H be a compactly causal symmetric space with causal compactification Φ : G∕H →Š1, where Š1 is the Bergman-Šilov boundary of a tube type domain G1∕K1. The Hardy space H2(C) of G∕H is the space of holomorphic functions on a domain Ξ(Co) ⊂ Gℂ∕Hℂ with L2-boundary values on G∕H. We extend Φ to imbed Ξ(Co) into G1∕K1, such that Ξ(Co) = {z ∈ G1∕K1∣ψm(z)≠0}, with ψm explicitly known. We use this to construct an isometry I of the classical Hardy space Hcl on G1∕K1 into H2(C) or into a Hardy space H2(C) defined on a covering Ξ(Co) of Ξ(Co). We describe the image of I in terms of the highest weight modulus occuring in the decomposition of the Hardy space. |
Milestones
Received: 29 December 1998
Published: 1 October 2001
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Authors |
| Frank Betten | |
| Universität Göttingen Mathematisches Institut Bunsenstraße 3–5, D–37073 Göttingen Germany |
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| Gestur Ólafsson | |
| Department of Mathematics Louisiana State University Baton Rouge, LA 70803 |
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