Том 71
№ 4

All Issues

Il’inskaya I. P.

Articles: 2
Brief Communications (Russian)

Probability Measures on the Group of Walsh Functions With Trivial Equivalence Class

Il’inskaya I. P., Neguritsa D. S.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2013. - 65, № 5. - pp. 717–721

We establish necessary and sufficient conditions for the retrieval, to within a shift, of a composition of three Poisson distributions and a uniform distribution on five or six elements of the group of Walsh functions according to the absolute values of their characteristic functions.

Article (Russian)

Arithmetic of semigroups of series in multiplicative systems

Il’inskaya I. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 7. - pp. 939–947

We study the arithmetic of a semigroup $\mathcal{M}_P$ of functions with operation of multiplication representable in the form $f(x)=∑^{∞}_{n=0} a_nχ_n(x)\left(a_n≥0,\; ∑^{∞}_{n=0}a_n =1 \right)$, where $\{χ_n|\}^{∞}_{n=0}$ is a system of multiplicative functions that are generalizations of the classical Walsh functions. For the semigroup $\mathcal{M}_P$ , analogs of the well-known Khinchin theorems related to the arithmetic of a semigroup of probability measures in $R_n$ are true. We describe the class $I_0(\mathcal{M}_P)$ of functions without indivisible or nondegenerate idempotent divisors and construct a class of indecomposable functions that is dense in $\mathcal{M}_P$ in the topology of uniform convergence.