Une nouvelle propriété des suites de Rudin-Shapiro
Une nouvelle propriété des suites de Rudin-Shapiro
The Rudin-Shapiro sequences have extremal properties in harmonic analysis. Using the fact that such a sequence is an automaton-sequence, we describe explicitely its spectrum (maximal spectral type, spectral multiplicity, multiplicity function). For example, we prove that the q-generalized Rudin-Shapiro sequence contains in its spectrum a Lebesgue-component, with multiplicity equal to …