Spectrum of a Rudin-Shapiro-like sequence

Abstract

We show that a recently proposed Rudin-Shapiro-like sequence, with balanced weights, has purely singular continuous diffraction spectrum, in contrast to the well-known Rudin-Shapiro sequence whose diffraction is absolutely continuous. This answers a question that had been raised about this new sequence.

arXiv comment7 pages

References in corpus (2)

• Mathematical diffraction of aperiodic structures
• Spectral Theory of Substitutions in ${\mathbb{Z}}^d$

Cited by in corpus (6)

• Singular substitutions of constant length
• Lyapunov exponents for binary substitutions of constant length
• Renormalisation of pair correlations and their Fourier transforms for primitive block substitutions
• Substitution-based structures with absolutely continuous spectrum
• Inflation versus projection sets in aperiodic systems: The role of the window in averaging and diffraction
• Correlation functions of the Rudin-Shapiro sequence