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

    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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