For a real bounded symmetric domain, G/K, we construct various natural enlargements to which several aspects of harmonic analysis on G/K and G have extensions. Our starting point is the realization of G/K as a totally real submanifold in a bounded domain G_h/K_h. We describe the boundary orbits and relate them to the boundary orbits of G_h/K_h. We relate the crown and the split-holomorphic crown of G/K to the crown \Xi_h of G_h/K_h. We identify an extension of a representation of K to a larger group L_c and use that to extend sections of vector bundles over the Borel compactification of G/K to its closure. Also, we show there is an analytic extension of K-finite matrix coefficients of G to a specific Matsuki cycle space.

中文翻译：

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实有界对称域的扩展

对于实数有界对称域 G/K，我们构建了各种自然扩展，对 G/K 和 G 的谐波分析的几个方面都有扩展。我们的出发点是将 G/K 实现为有界域 G_h/K_h 中完全真实的子流形。我们描述边界轨道并将它们与 G_h/K_h 的边界轨道联系起来。我们将 G/K 的冠和分裂全纯冠与 G_h/K_h 的冠 \Xi_h 联系起来。我们确定 K 的表示扩展到更大的群 L_c 并使用它来扩展 G/K 的 Borel 紧化上的向量丛的部分到它的闭包。此外，我们展示了 G 的 K 有限矩阵系数到特定 Matsuki 循环空间的解析扩展。