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Journal Article

Extensions of real bounded symmetric domains


Ólafsson,  Gestur
Max Planck Institute for Mathematics, Max Planck Society;


Stanton,  Robert J.
Max Planck Institute for Mathematics, Max Planck Society;

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Ólafsson, G., & Stanton, R. J. (2020). Extensions of real bounded symmetric domains. Journal of Functional Analysis, 279(8): 108709. doi:10.1016/j.jfa.2020.108709.

Cite as: http://hdl.handle.net/21.11116/0000-0007-029C-7
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.