Title

Martingales, Endomorphisms, And Covariant Systems Of Operators In Hilbert Space

Keywords

Cuntz algebra; Iterated function system (IFS); Julia set; Martingale; Multiresolution; Perron-Frobenius-Ruelle operator; Scaling function; Subshift; Transition probability; Wavelet

Abstract

In the theory of wavelets, in the study of subshifts, in the analysis of Julia sets of rational maps of a complex variable, and, more generally, in the study of dynamical systems, we are faced with the problem of building a unitary operator from a mapping r in a compact metric space X. The space X may be a torus, or the state space of subshift dynamical systems, or a Julia set. While our motivation derives from some wavelet problems, we have in mind other applications as well; and the issues involving covariant operator systems may be of independent interest. © Copyright by THETA, 2007.

Publication Date

9-1-2007

Publication Title

Journal of Operator Theory

Volume

58

Issue

2

Number of Pages

269-310

Document Type

Article

Personal Identifier

scopus

Socpus ID

42149167993 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/42149167993

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