Geodesic
Upper bounds for the concentration function in a Hilbert space
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 335-349 Cet article a éte moissonné depuis la source Math-Net.Ru

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New bounds (analogous to the bounds obtained by Kolmogorov, Rogozin and Esseen) are derived for the concentration function of the sums of independent random variables with values in a Hilbert space. In particular, the absolute constants used in the estimates don't depend on the dimension in the finite-dimensional space. Further, some limit theorems for the concentration function and some estimates for the concentration functions of infinitely divisible distributions are given. 
@article{TVP_1981_26_2_a6,
     author = {G. Siegel},
     title = {Upper bounds for the concentration function in {a~Hilbert} space},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {335--349},
     year = {1981},
     volume = {26},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a6/}
}
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G. Siegel. Upper bounds for the concentration function in a Hilbert space. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 2, pp. 335-349. http://geodesic.mathdoc.fr/item/TVP_1981_26_2_a6/