Geodesic
The analytical precising of the Heyde theorem on linear forms of independent random variables
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 54-59

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In terms of characteristic functions it is refined the theorem of Heyde on characteri3ization of the Gaussian distribution. 
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     author = {A. M. Kagan},
     title = {The analytical precising of the {Heyde} theorem on linear forms of independent random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {54--59},
     publisher = {mathdoc},
     volume = {166},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a6/}
}
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A. M. Kagan. The analytical precising of the Heyde theorem on linear forms of independent random variables. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 54-59. http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a6/