Arithmetic of semigroups of series in multiplicative systems
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 clas...
Збережено в:
| Дата: | 2009 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2009
|
| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/3068 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | 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. |
|---|