Une nouvelle propriété des suites de Rudin-Shapiro
Annales de l'Institut Fourier, Volume 37 (1987) no. 2, p. 115-138

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 qϕ(q).

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 qϕ(q).

@article{AIF_1987__37_2_115_0,
     author = {Queffelec, Martine},
     title = {Une nouvelle propri\'et\'e des suites de Rudin-Shapiro},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {37},
     number = {2},
     year = {1987},
     pages = {115-138},
     doi = {10.5802/aif.1089},
     zbl = {0597.10054},
     mrnumber = {88m:11060},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1987__37_2_115_0}
}
Queffelec, Martine. Une nouvelle propriété des suites de Rudin-Shapiro. Annales de l'Institut Fourier, Volume 37 (1987) no. 2, pp. 115-138. doi : 10.5802/aif.1089. http://www.numdam.org/item/AIF_1987__37_2_115_0/

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