Martingales, endomorphisms, and covariant systems of operators in Hilbert space
Abbreviated Journal Title
J. Operat. Theor.
wavelet; Julia set; subshift; Cuntz algebra; iterated function system; (IFS); Perron-Frobenius-Ruelle operator; multiresolution; Martingale; scaling function; transition probability; WAVELETS; MAPS; Mathematics
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 of Operator Theory
"Martingales, endomorphisms, and covariant systems of operators in Hilbert space" (2007). Faculty Bibliography 2000s. 7083.