Spectrum of a Rudin–Shapiro-like sequence

Lax Chan; Uwe Grimm

doi:10.1016/j.aam.2016.12.003

Spectrum of a Rudin–Shapiro-like sequence

Lax Chan
, Uwe Grimm

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	16-23
Number of pages	8
Journal	Advances in Applied Mathematics
Volume	87
DOIs	https://doi.org/10.1016/j.aam.2016.12.003
Publication status	Published - 1 Jun 2017
Externally published	Yes

Keywords

Bartlett's algorithm
Spectral measure
Substitution dynamical system

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10.1016/j.aam.2016.12.003

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title = "Spectrum of a Rudin{\textendash}Shapiro-like sequence",

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

keywords = "Bartlett's algorithm, Spectral measure, Substitution dynamical system",

author = "Lax Chan and Uwe Grimm",

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AU - Grimm, Uwe

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AB - 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.

KW - Bartlett's algorithm

KW - Spectral measure

KW - Substitution dynamical system

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DO - 10.1016/j.aam.2016.12.003

M3 - Article

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VL - 87

SP - 16

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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

ER -

Spectrum of a Rudin–Shapiro-like sequence

Abstract

Keywords

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