Geodesic
Contribution to the analytic theory of linear forms of independent random variables
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 153 (1986), pp. 37-44

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Characterizations of the Gaussian distribution through natural properties of linear forms of independent random variables are refined by replacing the $\sigma$-algebra generated by one form with a finite dimensional space of the polynomials in this form. 
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     author = {A. A. Zinger and A. M. Kagan},
     title = {Contribution to the analytic theory of linear forms of independent random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     publisher = {mathdoc},
     volume = {153},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_153_a3/}
}
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A. A. Zinger; A. M. Kagan. Contribution to the analytic theory of linear forms of independent random variables. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 153 (1986), pp. 37-44. http://geodesic.mathdoc.fr/item/ZNSL_1986_153_a3/