호남수학학술지 (Honam Mathematical Journal)

  • 제43권2호
  • /
  • Pages.259-267
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  • 2021
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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FOURIER SERIES OF A DEVIL'S STAIRCASE

  • Kwon, DoYong (Department of Mathematics, Chonnam National University)
  • 투고 : 2021.01.22
  • 심사 : 2021.03.25
  • 발행 : 2021.06.25
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초록

Given 𝛽 > 1, we consider real numbers whose 𝛽-expansions are Sturmian words. When the slope of Sturmian words varies, their behaviors have been well studied from analytical point of view. The regularity enables us to find the Fourier series expansion, while the singularity at rational slopes yields a new kind of trigonometric series representing 𝜋.

키워드

과제정보

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B02010219).

참고문헌

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