Перегляд за Автор "Vishnyakova, A.M."

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On a conjecture of Yu. V. Linnik
(1991) Vishnyakova, A.M.; Ostrovskii, I.V.; Ulanovskii, A.M.
A survey is given of work concerning Linnik's 1960 conjecture on the growth of entire characteristic functions (Fourier transforms) of probability measures. A proof of this conjecture is presented that is substantially shorter and more elementary than the known proofs. With the help of the same idea, new facts are established about the growth of entire characteristic functions with restrictions on the arguments of the zeros.
On the growth of ridge functions non-vanishing in an angular domain
(1997) Vishnyakova, A.M.
For an entire ridge function of finite order $\rho$ which is non-vanishing in the angle $\{z : |\arg z - \pi/2| < \alpha \} \cup \{z : |argz + \pi/2| < \alpha \}$, $0 < \alpha \le \pi/2$, the sharp estimate of $\rho $ in terms of $\alpha $ is obtained. Analogous result is obtained for ridge functions analytic in the upper half-plane.