A natural space of functions for the Ruelle operator theorem
A natural space of functions for the Ruelle operator theorem
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DOI：
10.1017/s0143385707000028
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发表时间：
2007-06
影响因子：
0.9
通讯作者：
P. Walters
中科院分区：
文献类型：
--
作者：
P. Walters
本文研究了0序列和1序列空间X$上的一个新的实值连续函数空间R（X）$。我们确切地表明，当Ruelle算子定理持有这样的功能。R（X）$中的任意g$-函数都有唯一的g$-测度，并且相应的转移算子的幂收敛.我们还表明弓$（X，T）\neq W（X，T）$和有界可测的coboundaries，这是不连续的coboundaries，为双序列的零和一的空间上的移位的存在。
We study a new space, $R(X)$, of real-valued continuous functions on the space $X$ of sequences of zeros and ones. We show exactly when the Ruelle operator theorem holds for such functions. Any $g$-function in $R(X)$ has a unique $g$-measure and powers of the corresponding transfer operator converge. We also show Bow$(X,T)\neq W(X,T)$ and relate this to the existence of bounded measurable coboundaries, which are not continuous coboundaries, for the shift on the space of bi-sequences of zeros and ones.