论文标题
函数与实数和指数高高的全局功能一致的功能一致
Functions consistent with real numbers, and global extrema of functions in exponential Takagi class
论文作者
论文摘要
The functions of the Takagi exponential class are similar in construction to the continuous, nowhere differentiable Takagi function described in 1901. They have one real parameter $v\in (-1;1)$ and at points $x\in{\mathbb R}$ are defined by the series $T_v(x) = \sum_{n=0}^\infty v^n T_0(2^nx)$, where $ t_0（x）$是$ x $和最近整数点之间的距离。如果$ v = 1/2 $，则$ t_v $与高吉的功能重合。在本文中，对于参数$ v $的不同值，我们研究了功能的全球极端$ t_v $以及一组极端点。 $ t_v $的所有功能的期限为$ 1 $，因此仅在细分市场上进行调查[0; 1] $。这项研究基于一致和反矛盾的多项式和序列的特性，该工作的前半部分是专门的。
The functions of the Takagi exponential class are similar in construction to the continuous, nowhere differentiable Takagi function described in 1901. They have one real parameter $v\in (-1;1)$ and at points $x\in{\mathbb R}$ are defined by the series $T_v(x) = \sum_{n=0}^\infty v^n T_0(2^nx)$, where $T_0(x)$ is the distance between $x$ and the nearest integer point. If $v=1/2$ then $T_v$ coincides with Takagi's function. In this paper, for different values of the parameter $v$, we study the global extremes of the functions $T_v$, as well as the sets of extreme points. All functions of $T_v$ have a period of $1$, so they are investigated only on the segment $[0;1]$. This study is based on the properties of consistent and anti-consistent polynomials and series, which the first half of the work is devoted to.
