Geodesic
On~the~uniqueness of supports of analytic functionals
Izvestiya. Mathematics , Tome 39 (1992) no. 3, pp. 1129-1149

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This paper describes a class of convex compact sets $K$ in $\mathbf C^n$ having the following uniqueness property: $K$ is the unique support of every analytic functional for which it is a support. 
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     author = {A. S. Krivosheev},
     title = {On~the~uniqueness of supports of analytic functionals},
     journal = {Izvestiya. Mathematics },
     pages = {1129--1149},
     publisher = {mathdoc},
     volume = {39},
     number = {3},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_39_3_a2/}
}
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A. S. Krivosheev. On~the~uniqueness of supports of analytic functionals. Izvestiya. Mathematics , Tome 39 (1992) no. 3, pp. 1129-1149. http://geodesic.mathdoc.fr/item/IM2_1992_39_3_a2/