Ruelle Operators

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

Introduction

1

(6)

A discrete ax + b group

7

(6)

Proof of Theorem 2.4

13

(10)

Wavelet filters

23

(10)

Cocycle equivalence of filter functions

33

(5)

The transfer operator of Keane

38

(9)

A representation theorem for R-harmonic functions

47

(6)

Signed solutions to R(f) = f

53

(5)

Bibliography

58

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