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

By Dorin Ervin Dutkay, Palle E. T. Jorgensen. 2004

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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.

Subfields: Applied Mathematics, Mathematical Physics

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