Developments in Non-Integer Bases
Developments in Non-Integer Bases
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DOI：
10.1023/a:1006557705401
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发表时间：
1998-04
影响因子：
0.9
通讯作者：
P. Erdös;V. Komornik
中科院分区：
文献类型：
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作者：
P. Erdös;V. Komornik
我们证明了各种定理的发展，在非整数基础。我们在这里提到其中两个，它们回答了几年前提出的一些问题。首先确定一个真实的数q> 1，并考虑那些真实的数y的递增序列0 = yo < y1 < y2 <，这些数至少有一个表示形式y = ε0 + ε 1 q ++ εnqn，其中某个整数n ≥ 0，系数ε，E {0，1}。其次，对于每个充分接近1的q，存在一个0和1的序列（εi），满足= 1，包含数字0和1的所有可能的有限变化。
We prove various theorems concerning the developments in non-integer bases. We mention two of them here, which answer some questions formulated several years ago. First fix a real number q> 1 and consider the increasing sequence 0 = yo < y1 < y2 < ¨ of those real numbers y which have at least one representation of the form y = ε0 + ε1q + ¨ + εnqn with some integer n ≧ 0 and coefficients ε, Ε {0, 1}. Then the difference sequence yk+1-yk tends to 0 for all q, sufficiently close to 1.Secondly, for each q, sufficiently close to 1, there exists a sequence (εi) of zeroes and ones, satisfying= 1 and containing all possible finite variations of the digits 0 and 1.