Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator

Released on by Palle E. T. Jørgensen
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  • Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator Book Detail

  • Author : Palle E. T. Jørgensen
  • Release Date : 2001
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 74
  • ISBN 13 : 0821826883
  • File Size : 10,10 MB
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Ruelle Operators: Functions which Are Harmonic with Respect to a Transfer Operator by Palle E. T. Jørgensen PDF Summary

Book Description: Let $N\in\mathbb{N}$, $N\geq2$, be given. Motivated by wavelet analysis, this title considers a class of normal representations of the $C DEGREES{\ast}$-algebra $\mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU DEGREES{-1}=V DEGREES{N}$. The representations are in one-to-one correspondence with solutions $h\in L DEGREES{1}\left(\mathbb{T}\right)$, $h\geq0$, 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

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Ruelle Operators

Ruelle Operators

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Introduction A discrete $ax+b$ group Proof of Theorem 2.4 Wavelet filters Cocycle equivalence of filter functions The transfer operator of Keane A representatio