Ruelle operators : functions which are harmonic with respect to a transfer operator
著者
書誌事項
Ruelle operators : functions which are harmonic with respect to a transfer operator
（Memoirs of the American Mathematical Society, no. 720）
American Mathematical Society, 2001
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注記
"July 2001, volume 152, number 720 (first of 5 numbers)"
Includes bibliographical references (p. 58-60)
内容説明・目次
内容説明
Let $N\in\mathbb{N}$, $N\geq2$, be given. Motivated by wavelet analysis, we consider a class of normal representations of the $C^{\ast}$-algebra $\mathfrak {A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU^{-1}=V^{N}$. The representations are in one-to-one correspondence with solutions $h\in L^{1}\left(\mathbb{T}\right)$, $h\geq0$, to $R\left(h\right)=h$ where $R$ is a certain transfer operator (positivity-preserving) which was studied previously by D. Ruelle. The representations of $\mathfrak {A}_{N}$ may also be viewed as representations of a certain (discrete) $N$-adic $ax+b$ group which was considered recently by J.-B. Bost and A. Connes.
目次
Introduction A discrete $ax+b$ group Proof of Theorem 2.4 Wavelet filters Cocycle equivalence of filter functions The transfer operator of Keane A representation theorem for $R$-harmonic functions Signed solutions to $R(f)=f$ Bibliography.
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