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Zbl 0597.10054
Queffelec, Martine
Une nouvelle propriété des suites de Rudin-Shapiro. (A new property of Rudin-Shapiro sequences). (French)
[J] Ann. Inst. Fourier 37, No.2, 115-138 (1987). ISSN 0373-0956; ISSN 1777-5310/e

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 2000:: *11K55 Metric theory of other number-theoretic algorithms and expansions
42A05 Trigonometric polynomials
28D05 Measure-preserving transformations

Keywords: Rudin-Shapiro sequences; extremal properties; automaton sequence; spectrum; maximal spectral type; spectral multiplicity; multiplicity function; q-generalized Rudin-Shapiro sequence; substitution; dynamical system; Riesz products

Cited in: Zbl 0901.11010

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