Mathematical Sciences: Harmonic Analysis on Causal Symmetric Spaces

9626541奥拉夫松这个建议涉及对称空间上的调和分析领域。更具体地说，它与因果对称空间上的调和分析和表示理论有关。研究人员计划研究球面拉普拉斯变换的Paley-Wiener定理；因果紧化及其与管域上Hardy空间的关系；对偶实形式之间么正表示的解析延拓。因果对称空间，以及更一般的因果流形，都是以时空连续体为模型的。因果对称空间有两个明显的特征：在因果流形上定义了时间方向；保持这种时间结构的对称性在研究它们中起着主导作用。

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.