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MARTINGALES, ENDOMORPHISMS, AND COVARIANT SYSTEMS OF OPERATORS IN HILBERT SPACE

DORIN ERVIN DUTKAY and PALLE E.T. JORGENSEN
Journal of Operator Theory
Vol. 58, No. 2 (Fall 2007), pp. 269-310
Published by: Theta Foundation
Stable URL: http://www.jstor.org/stable/24715796
Page Count: 42
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
MARTINGALES, ENDOMORPHISMS, AND COVARIANT SYSTEMS OF OPERATORS IN HILBERT SPACE
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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.

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