Geodesic
On a~group analogue of a~theorem of~A.\,M.~Kagan
Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 180-183

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The well-known Darmois–Skitovich theorem characterizing the Gaussian distribution on the real line by the independence of two linear statistics was generalized by A. M. Kagan to the case of several linear forms. In the present paper A. M. Kagan's theorem is proved for a wide class of locally compact Abelian groups.
Keywords: Gaussian distribution, locally compact Abelian group, joint distribution of linear forms. 
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     author = {S. V. Lisyanoi},
     title = {On a~group analogue of a~theorem {of~A.\,M.~Kagan}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {180--183},
     publisher = {mathdoc},
     volume = {40},
     number = {1},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a12/}
}
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S. V. Lisyanoi. On a~group analogue of a~theorem of~A.\,M.~Kagan. Teoriâ veroâtnostej i ee primeneniâ, Tome 40 (1995) no. 1, pp. 180-183. http://geodesic.mathdoc.fr/item/TVP_1995_40_1_a12/