Causal Compactification and Hardy Spaces for Spaces of Hermitian Type
نویسنده
چکیده
Let G/H be a compactly causal symmetric space with causal compactification Φ : G/H → Š1, where Š1 is the BergmanŠilov 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(C) ⊂ GC/HC with L-boundary values on G/H. We extend Φ to imbed Ξ(C) into G1/K1, such that Ξ(C) = {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 H̃2(C) defined on a covering Ξ̃(C) of Ξ(C). We describe the image of I in terms of the highest weight modulus occuring in the decomposition of the Hardy space.
منابع مشابه
Causal Compactification of Compactly Causal Spaces
We give a classification of causal compactifications of compactly causal spaces. Introduced by Ólafsson and Ørsted, for a compactly causal space G/H, these compactifications are given by G-orbits in the BergmanŠilov boundary of G1/K1, with G ⊂ G1 and (G1,K1, θ) a Hermitian symmetric space of tube type. For the classical spaces an explicit construction is presented.
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