论文标题
一些与奇数部分商的持续分数扩展的渐近结果
Some asymptotic results for the continued fraction expansions with odd partial quotients
论文作者
论文摘要
我们介绍并开发了不同的方法来研究分布函数在奇数持续分数中的渐近行为。首先，通过考虑马尔可夫链的过渡操作员与这些扩展相关联，这些扩展在界变异的复杂值函数的某个BANACH空间上，对Gauss-Kuzmin型问题中的解决方案进行了简要调查。其次，我们使用szüsz方法获得类似的渐近结果，并对涉及的收敛速率进行良好的估计。
We present and develop different approaches to study the asymptotic behavior of the distribution functions in the odd continued fractions case. Firstly, by considering the transition operator of the Markov chain associated with these expansions on a certain Banach space of complex-valued functions of bounded variation we make a brief survey of the solution in the Gauss-Kuzmin-type problem. Secondly, we use the method of Szüsz to obtain a similar asymptotic result and to give a good estimate of the convergence rate involved.
