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Une nouvelle propriété des suites de Rudin-Shapiro. (A new property of Rudin-Shapiro sequences). (French) Zbl 0597.10054
The Rudin-Shapiro sequences have extremal properties in harmonic analysis. Using the fact that such a sequence is an automaton sequence, we describe explicitly 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 q \(\phi\) (q).

MSC:
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
42A05 Trigonometric polynomials, inequalities, extremal problems
28D05 Measure-preserving transformations
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References:
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