Dynamical properties of endomorphisms, multiresolutions, similarity-and orthogonality relations

2016/07/25 by Palle E. T. Jørgensen, Feng Tian, Jorgensen, Palle +1
Computer Science · Mathematics · #46N30 #47L60 #58J65 #60H07 #65R10 #81S25 #81S40 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Primary 81S20 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1607.07229

openalex publication_date 2016/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study positive transfer operators R in the setting of general measure spaces (X,\mathscrB). For each R, we compute associated path-space probability spaces (Ω,ℙ). When the transfer operator R is compatible with an endomorphism in (X,\mathscrB), we get associated multiresolutions for the Hilbert spaces L²(Ω,ℙ) where the path-space Ω may then be taken to be a solenoid. Our multiresolutions include both orthogonality relations and self-similarity algorithms for standard wavelets and for generalized wavelet-resolutions. Applications are given to topological dynamics, ergodic theory, and spectral theory, in general; to iterated function systems (IFSs), and to Markov chains in particular.

Citations

• Subalgebras of C*-algebras
• Covariant representations for matrix-valued transfer operators

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