Numeral system with two bases having different signs and related special functions
We consider an analytic system of encoding of numbers ($G_2$-representative) from an interval $[0;g_0]$ by means of the two-symbol alphabet $A\equiv\{0;1\}$ with two bases having different signs: $g_0\in(0;1)$ and $g_1=g_0-1$.The system is based on expansion of the numerical series. Functions with n...
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| Дата: | 2020 |
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| Ключові слова: | keywords |
| Автори: | , , , , , , , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://trim.imath.kiev.ua/index.php/trim/article/view/395 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Репозитарії
Transactions of Institute of Mathematics of NAS of Ukraine| Резюме: | We consider an analytic system of encoding of numbers ($G_2$-representative) from an interval $[0;g_0]$ by means of the two-symbol alphabet $A\equiv\{0;1\}$ with two bases having different signs: $g_0\in(0;1)$ and $g_1=g_0-1$.The system is based on expansion of the numerical series. Functions with non-homogeneous local properties of structural and differential kind are studied. Inversor of digits of the $G_2$-representation of the numbers and shift operator for the $G_2$-representation are among them.Properties of these functions are found out being rather surprising: the inversor is not a monotonic function and the shift operator is a continuous function. This implies the fundamental difference between the present and previously studied representations.We compare properties of the $G_2$- and two-base $Q_2$-representations (both are positive) using the projector of digits of between them. |
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