Title

Martingales, endomorphisms, and covariant systems of operators in Hilbert space

Authors

Authors

D. E. Dutkay;P. E. T. Jorgensen

Comments

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Abbreviated Journal Title

J. Operat. Theor.

Keywords

wavelet; Julia set; subshift; Cuntz algebra; iterated function system; (IFS); Perron-Frobenius-Ruelle operator; multiresolution; Martingale; scaling function; transition probability; WAVELETS; MAPS; Mathematics

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.

Journal Title

Journal of Operator Theory

Volume

58

Issue/Number

2

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

269

Last Page

310

WOS Identifier

WOS:000253321000003

ISSN

0379-4024

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