论文标题
多维持续部分的功能分析：第二部分
Functional analysis behind a Family of Multidimensional Continued Fractions: Part II
论文作者
论文摘要
本文直接延续了“多维持续分数背后的功能分析：第一部分”，在该家族中，我们开始探索三角分区图的转移操作员背后的功能分析，该家族包括许多（如果不是大多数，众所周知的多维持续持续分数）。这使我们现在可以找到与指定的Banach空间上选择的三角分区图相关的转移操作员特征值1的本本特征。我们继续证明，转移操作员被视为作用于希尔伯特空间的一维家族，与精选的三角分区图相关的是Trace Class Zero的核。我们通过得出与选择的三角分区图关联的高斯-Kuzmin分布来结束。
This paper is a direct continuation of "Functional analysis behind a Family of Multidimensional Continued Fractions: Part I," in which we started the exploration of the functional analysis behind the transfer operators for triangle partition maps, a family that includes many, if not most, well-known multidimensional continued fraction algorithms. This allows us now to find eigenfunctions of eigenvalue 1 for transfer operators associated with select triangle partition maps on specified Banach spaces. We proceed to prove that the transfer operators, viewed as acting on one-dimensional families of Hilbert spaces, associated with select triangle partition maps are nuclear of trace class zero. We finish by deriving Gauss-Kuzmin distributions associated with select triangle partition maps.
