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Une nouvelle propriété des suites de Rudin-Shapiro

Martine Queffelec (1987)

Annales de l'institut Fourier

Les suites de Rudin-Shapiro ont des propriétés extrémales en analyse harmonique. En remarquant qu’une telle suite est reconnaissable par un automate fini, nous en décrivons explicitement le spectre (type spectral maximal, multiplicité spectrale fonction multiplicité). Nous établissons par exemple, que la suite de Rudin-Shapiro généralisée à l’ordre q contient dans son spectre une composante de Lebesgue, de multiplicité q φ ( q ) .

Unique Bernoulli g -measures

Anders Johansson, Anders Öberg, Mark Pollicott (2012)

Journal of the European Mathematical Society

We improve and subsume the conditions of Johansson and Öberg and Berbee for uniqueness of a g -measure, i.e., a stationary distribution for chains with complete connections. In addition, we prove that these unique g -measures have Bernoulli natural extensions. We also conclude that we have convergence in the Wasserstein metric of the iterates of the adjoint transfer operator to the g -measure.

Uniqueness of a martingale-coboundary decomposition of stationary processes

Pavel Samek, Dalibor Volný (1992)

Commentationes Mathematicae Universitatis Carolinae

In the limit theory for strictly stationary processes f T i , i , the decomposition f = m + g - g T proved to be very useful; here T is a bimeasurable and measure preserving transformation an ( m T i ) is a martingale difference sequence. We shall study the uniqueness of the decomposition when the filtration of ( m T i ) is fixed. The case when the filtration varies is solved in [13]. The necessary and sufficient condition of the existence of the decomposition were given in [12] (for earlier and weaker versions of the results see [7])....

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