Mathematical Sciences: Harmonic Analysis on Causal Symmetric Spaces

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9626541 Olafsson This proposal lies in the area of harmonic analysis on symmetric spaces. More specifically, it has to do with harmonic analysis and representation theory on causal symmetric spaces. The investigator plans to study Paley-Wiener theorems for the spherical Laplace transform; causal compactification and the relation to Hardy spaces on tube domains; analytic continuation of unitary representations between dual real forms. Causal symmetric spaces, and more generally, causal manifolds, are modeled after the space-time continuum. There are two distinguishing feature about causal symmetric spaces: a temporal orientation is defined on a causal manifold; symmetries preserving this temporal structure play a dominant role in studying them.