# Ruelle Operators: Functions Which are Harmonic with Respect to a Transfer Operator (Memoirs of the American Mathematical Society)

Paperback

Up to 2 WeeksUsually despatched within 2 weeks

£48.50

### Description

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.

### Contents

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.

### Product Details

• ISBN13: 9780821826881
• Format: Paperback
• ID: 9780821826881
• ISBN10: 0821826883

### Delivery Information

• Saver Delivery: Yes
• 1st Class Delivery: Yes
• Courier Delivery: Yes
• Store Delivery: Yes

### Calculus and AnalysisView More

Prices are for internet purchases only. Prices and availability in WHSmith Stores may vary significantly

Close