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Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator
 
Palle E. T. Jorgensen University of Iowa, Iowa City, IA
Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator
eBook ISBN:  978-1-4704-0313-3
Product Code:  MEMO/152/720.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator
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Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator
Palle E. T. Jorgensen University of Iowa, Iowa City, IA
eBook ISBN:  978-1-4704-0313-3
Product Code:  MEMO/152/720.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $29.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1522001; 60 pp
    MSC: Primary 46; 42; 43; Secondary 41;

    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.

    Readership

    Graduate students and research mathematicians interested in functional analysis.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. A discrete $ax + b$ group
    • 3. Proof of Theorem 2.4
    • 4. Wavelet filters
    • 5. Cocycle equivalence of filter functions
    • 6. The transfer operator of Keane
    • 7. A representation theorem for $R$-harmonic functions
    • 8. Signed solutions to $R(f) = f$
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1522001; 60 pp
MSC: Primary 46; 42; 43; Secondary 41;

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.

Readership

Graduate students and research mathematicians interested in functional analysis.

  • Chapters
  • 1. Introduction
  • 2. A discrete $ax + b$ group
  • 3. Proof of Theorem 2.4
  • 4. Wavelet filters
  • 5. Cocycle equivalence of filter functions
  • 6. The transfer operator of Keane
  • 7. A representation theorem for $R$-harmonic functions
  • 8. Signed solutions to $R(f) = f$
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.