Geodesic
On functions of bounded variation that are determined by restriction to a semiaxi
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 427-436 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $F(x)$, $x\in\mathbf R$, be a function of bounded variation on the line. This paper investigates whether convolutions of the form $F(x/a_1)*\dots*F(x/a_n)$, $n\geqslant2$, are uniquely determined from their values on the semiaxis $x\in(-\infty,0)$. As a corollary to one of the results a conjecture of Kruglov is proved: if $F(x)$ is a distribution function, $\Phi (x)$ is the standard normal distribution function, and $a_1>0,\dots,a_n>0$, $n\geqslant2$, then the equality $$ F\biggl(\frac x{a_1}\biggr)*\dots*F\biggl(\frac x{a_n}\biggr)=\Phi(x),\qquad x\in(-\infty,0), $$ implies that $F(x)\equiv\Phi((a^2_1+\dots+a^2_n)^{1/2}x)$. Bibliography: 10 titles. 
@article{SM_1988_60_2_a11,
     author = {A. M. Ulanovskii},
     title = {On~functions of bounded variation that are determined by restriction to a~semiaxi},
     journal = {Sbornik. Mathematics},
     pages = {427--436},
     year = {1988},
     volume = {60},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_60_2_a11/}
}
TY  - JOUR
AU  - A. M. Ulanovskii
TI  - On functions of bounded variation that are determined by restriction to a semiaxi
JO  - Sbornik. Mathematics
PY  - 1988
SP  - 427
EP  - 436
VL  - 60
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1988_60_2_a11/
LA  - en
ID  - SM_1988_60_2_a11
ER  - 
%0 Journal Article
%A A. M. Ulanovskii
%T On functions of bounded variation that are determined by restriction to a semiaxi
%J Sbornik. Mathematics
%D 1988
%P 427-436
%V 60
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1988_60_2_a11/
%G en
%F SM_1988_60_2_a11
A. M. Ulanovskii. On functions of bounded variation that are determined by restriction to a semiaxi. Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 427-436. http://geodesic.mathdoc.fr/item/SM_1988_60_2_a11/

[1] Rossberg H.-J., “On a problem of Kolmogorov concerning the normal distribution”, Teoriya veroyatnostei i ee primeneniya, 19:4 (1974), 795–798 | MR | Zbl

[2] Riedel M. N., “On the one-sided tails of infinitely divisible distributions”, Math. Nachr., 70 (1975), 155–163 | DOI | MR | Zbl

[3] Ibragimov I. A., “Ob opredelenii bezgranichno delimoi funktsii raspredeleniya po ee znacheniyam na polupryamoi”, Teoriya veroyatnostei i ee primeneniya, 22:2 (1977), 393–399 | Zbl

[4] Titov A. N., “Ob opredelenii svertki odinakovykh funktsii raspredeleniya po ee znacheniyam na polupryamoi”, Teoriya veroyatnostei i ee primeneniya, 26:3 (1981), 610–611 | MR | Zbl

[5] Blank N. M., “O raspredeleniyakh, svertki kotorykh sovpadayut na poluosi”, Teoriya funktsii, funktsion. analiz i ikh pril., 41, Kharkov, 1984, 17–25 | MR | Zbl

[6] Ostrovskii I. V., “Ob odnom klasse funktsii ogranichennoi variatsii na pryamoi, opredelyaemykh svoimi znacheniyami na polupryamoi”, Zap. nauchn. seminarov LOMI, 92, 1979, 220–229 | MR | Zbl

[7] Ostrovskii I. V., “Generalization of the Titchmarsh convolution theorem and the complex-valued measures uniquely determined by their restriction to a half-line”, Lecture Notes in Math., 1155, 1985, 256–284 | MR

[8] Gordon A. Ya., Levin B. Ya., “O delenii kvazipolinomov”, Funktsion. analiz i ego pril., 5:1 (1971), 22–29 | MR | Zbl

[9] Ronkin A. L., “O neprivodimosti kvazipolinomov”, Teoriya funktsii, funktsion. analiz i ikh pril., 39, Kharkov, 1983, 106–110 | MR | Zbl

[10] Linnik Yu. V., Ostrovskii I. V., Razlozheniya sluchainykh velichin i vektorov, Nauka, M., 1972 | MR