Substitution-based structures with absolutely continuous spectrum

Lax Chan; Uwe Grimm; Ian Short

doi:10.1016/j.indag.2018.05.009

Substitution-based structures with absolutely continuous spectrum

Lax Chan
, Uwe Grimm
, Ian Short

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have a purely absolutely continuous diffraction measure and a mixed dynamical spectrum, with absolutely continuous and pure point parts. We discuss several examples, including a construction based on Fourier matrices which yields constant-length substitutions for any length.

Lingua originale	Inglese
pagine (da-a)	1072-1086
Numero di pagine	15
Rivista	Indagationes Mathematicae
Volume	29
Numero di pubblicazione	4
DOI	https://doi.org/10.1016/j.indag.2018.05.009
Stato di pubblicazione	Pubblicato - ago 2018
Pubblicato esternamente	Sì

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10.1016/j.indag.2018.05.009

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title = "Substitution-based structures with absolutely continuous spectrum",

abstract = "By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have a purely absolutely continuous diffraction measure and a mixed dynamical spectrum, with absolutely continuous and pure point parts. We discuss several examples, including a construction based on Fourier matrices which yields constant-length substitutions for any length.",

keywords = "Absolute continuity, Lebesgue spectrum, Spectral measure, Substitution dynamical system",

author = "Lax Chan and Uwe Grimm and Ian Short",

note = "Publisher Copyright: {\textcopyright} 2018 Royal Dutch Mathematical Society (KWG)",

year = "2018",

month = aug,

doi = "10.1016/j.indag.2018.05.009",

language = "English",

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journal = "Indagationes Mathematicae",

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T1 - Substitution-based structures with absolutely continuous spectrum

AU - Chan, Lax

AU - Grimm, Uwe

AU - Short, Ian

PY - 2018/8

Y1 - 2018/8

N2 - By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have a purely absolutely continuous diffraction measure and a mixed dynamical spectrum, with absolutely continuous and pure point parts. We discuss several examples, including a construction based on Fourier matrices which yields constant-length substitutions for any length.

AB - By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have a purely absolutely continuous diffraction measure and a mixed dynamical spectrum, with absolutely continuous and pure point parts. We discuss several examples, including a construction based on Fourier matrices which yields constant-length substitutions for any length.

KW - Absolute continuity

KW - Lebesgue spectrum

KW - Spectral measure

KW - Substitution dynamical system

UR - https://www.scopus.com/pages/publications/85048708738

U2 - 10.1016/j.indag.2018.05.009

DO - 10.1016/j.indag.2018.05.009

M3 - Article

SN - 0019-3577

VL - 29

SP - 1072

EP - 1086

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 4

ER -

Substitution-based structures with absolutely continuous spectrum

Abstract

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