Abstract

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(C^o) ⊂ G_C ∕ H_C with L²-boundary values on G ∕ H. We extend Φ to imbed Ξ(C^o) into G₁ ∕ K₁, such that Ξ(C^o) = {z in G₁ ∕ K₁ | ψ_m(z)≠0}, with ψ_m explicitly known. We use this to construct an isometry I of the classical Hardy space H_cl on G₁ ∕ K₁ into H₂(C) or into a Hardy space H₂(C) defined on a covering Ξ(C^o) of Ξ(C^o). We describe the image of I in terms of the highest weight modulus occuring in the decomposition of the Hardy space.

Authors