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 -generalized Rudin-Shapiro sequence contains in its spectrum a Lebesgue-component, with multiplicity equal to .
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 contient dans son spectre une composante de Lebesgue, de multiplicité .
@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}, pages = {115--138}, publisher = {Imprimerie Durand}, address = {28 - Luisant}, volume = {37}, number = {2}, year = {1987}, doi = {10.5802/aif.1089}, zbl = {0597.10054}, mrnumber = {88m:11060}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1089/} }
TY - JOUR TI - Une nouvelle propriété des suites de Rudin-Shapiro JO - Annales de l'Institut Fourier PY - 1987 DA - 1987/// SP - 115 EP - 138 VL - 37 IS - 2 PB - Imprimerie Durand PP - 28 - Luisant UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1089/ UR - https://zbmath.org/?q=an%3A0597.10054 UR - https://www.ams.org/mathscinet-getitem?mr=88m:11060 UR - https://doi.org/10.5802/aif.1089 DO - 10.5802/aif.1089 LA - fr ID - AIF_1987__37_2_115_0 ER -
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. https://aif.centre-mersenne.org/articles/10.5802/aif.1089/
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