Geodesic
The extended matrix disk is a domain of holomorphy
Izvestiya. Mathematics , Tome 38 (1992) no. 3, pp. 637-645

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It is proved that the extended matrix disk is a domain of holomorphy. This gives a positive answer to a conjecture that is a “compact” analogue of the conjecture on the extended future tube. 
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     author = {A. G. Sergeev and P. Heinzner},
     title = {The extended matrix disk is a domain of holomorphy},
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A. G. Sergeev; P. Heinzner. The extended matrix disk is a domain of holomorphy. Izvestiya. Mathematics , Tome 38 (1992) no. 3, pp. 637-645. http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a9/