Geodesic
On the factorization of infinitely divisible distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 661-664

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The article deals with the necessary and sufficient condition under which the infinitely divisible law $F$ having the finite spectral Levy's measure $\mu$ which is concentrated on the set of positive rational numbers and $$ \mu([y,\infty))=O\{\exp(-Ky^2)\},\quad y\to+\infty,\quad\exists K>0, $$ belongs to $I_0$. The following result is also established: if $F\in I_0$ and $(\alpha\in(0,1))$ $$ \varliminf_{r\to0}\ln\mu([\alpha r,r])/\ln(1/|r|)>1, $$ then $F$ belongs to Linnik's class $\mathfrak E$. 
@article{TVP_1975_20_3_a18,
     author = {A. E. Fryntov},
     title = {On the factorization of infinitely divisible distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {661--664},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a18/}
}
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A. E. Fryntov. On the factorization of infinitely divisible distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 3, pp. 661-664. http://geodesic.mathdoc.fr/item/TVP_1975_20_3_a18/