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MULTIFRACTAL ANALYSIS OF GENERALIZED THUE-MORSE TRIGONOMETRIC POLYNOMIALS

Fan, Aihua ; Schmeling, Jörg LU and Shen, Weixiao (2023) In Asian Journal of Mathematics 27(4). p.589-620
Abstract

We consider the generalized Thue-Morse sequences [Formula Presented] being a parameter) defined by [Formula Presented], where s2(n) is the sum of digits of the binary expansion of n. For the polynomials [Formula Presented] we have proved in [18] that the uniform norm [Formula Presented] behaves like Nγ(c)and the best exponent γ(c) is computed. In this paper, we study the pointwise behavior and give a complete multifractal analysis of the limit [Formula Presented].

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Generalized Thue-Morse sequences, Hausdorff dimension, Multifractal analysis
in
Asian Journal of Mathematics
volume
27
issue
4
pages
32 pages
publisher
International Press, Inc.
external identifiers
  • scopus:85199378876
ISSN
1093-6106
DOI
10.4310/AJM.2023.v27.n4.a6
language
English
LU publication?
yes
id
17c0538d-aeb9-45a8-9ff8-ded48ff7ee3a
date added to LUP
2024-12-12 12:49:01
date last changed
2025-04-04 14:04:48
@article{17c0538d-aeb9-45a8-9ff8-ded48ff7ee3a,
  abstract     = {{<p>We consider the generalized Thue-Morse sequences [Formula Presented] being a parameter) defined by [Formula Presented], where s<sub>2</sub>(n) is the sum of digits of the binary expansion of n. For the polynomials [Formula Presented] we have proved in [18] that the uniform norm [Formula Presented] behaves like N<sup>γ(c)</sup>and the best exponent γ(c) is computed. In this paper, we study the pointwise behavior and give a complete multifractal analysis of the limit [Formula Presented].</p>}},
  author       = {{Fan, Aihua and Schmeling, Jörg and Shen, Weixiao}},
  issn         = {{1093-6106}},
  keywords     = {{Generalized Thue-Morse sequences; Hausdorff dimension; Multifractal analysis}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{589--620}},
  publisher    = {{International Press, Inc.}},
  series       = {{Asian Journal of Mathematics}},
  title        = {{MULTIFRACTAL ANALYSIS OF GENERALIZED THUE-MORSE TRIGONOMETRIC POLYNOMIALS}},
  url          = {{http://dx.doi.org/10.4310/AJM.2023.v27.n4.a6}},
  doi          = {{10.4310/AJM.2023.v27.n4.a6}},
  volume       = {{27}},
  year         = {{2023}},
}