Extensions of real bounded symmetric domains

Ólafsson, Gestur; Stanton, Robert J.

doi:10.1016/j.jfa.2020.108709

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Extensions of real bounded symmetric domains

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

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

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https://doi.org/10.1016/j.jfa.2020.108709
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Citation

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: https://hdl.handle.net/21.11116/0000-0007-029C-7

Abstract

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.