On the relaxation time of Gauss' continued-fraction map. II. The Banach space approach (transfer operator method)
On the relaxation time of Gauss' continued-fraction map. II. The Banach space approach (transfer operator method)
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关于高斯连分数图的弛豫时间。
DOI：
10.1007/bf01022997
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
G. Roepstorff
中科院分区：
文献类型：
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作者：
D. Mayer;G. Roepstorff
当mapTx=1/x−[1/x]的迁移算子f(x)=f·T(x)的共轭算子u *被限制在本文第1部分引入的Hilbert空间h （υ）时，其谱与Koopman的等距算子f(x)的共轭算子u *的谱重合。如果n表示算子_ - p1with_（投影到特征函数上）对特征函数的支配特征值λ1=1，则−n__0正算子对某锥有一个支配正的、简单的特征值−λ2。对于λ2和mapT的松弛时间，存在一个极大极小原理，给出了严格的上界和下界。
The spectrum of the transfer operator ℒ for the mapTx=1/x−[1/x] when restricted to a certain Banach space of holomorphic functions is shown to coincide with the spectrum of the adjointU* of Koopman's isometric operatorUf(x)=f·T(x) when the former is restricted to the Hilbert space ℋ(υ) introduced in part I of this work. IfNdenotes the operator ℒ−P1withP1the projector onto the eigenfunction to the dominant eigenvalueλ1=1 of ℒ, then −Nis au0-positive operator with respect to some cone and therefore has a dominant positive, simple eigenvalue −λ2. A minimax principle holds giving rigorous upper and lower bounds both forλ2and the relaxation time of the mapT.