논문KCI 등재
Differentiability and non-differentiability points of the Minkowski question mark function
대한수학회 (The Korean Mathematical Society)|2016.10|대한수학회논문집 (Communications of the KMS)|제31권 제4호|pp. 811-817
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주제분류수학
초록
Using the periodic continued fraction, we give concrete examples of the points at which the derivatives of the Minkowski question mark function does not exist. We also give examples of the differentiability points which show that recent apparently independent results are consistent and closely related.
Abstract
Using the periodic continued fraction, we give concrete examples of the points at which the derivatives of the Minkowski question mark function does not exist. We also give examples of the differentiability points which show that recent apparently independent results are consistent and closely related.
참고문헌 (8)
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- M. Kessebohmer, "A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates", J. Reine Angew. Math, 605, pp.133~163 (2007)
- M. Kessebohmer, "Fractal analysis for sets of non-differentiability of Minkowski’s question mark function", J. Number Theory, 128(9), pp.2663~2686 (2008)
- Yeo-Rin Lee, "SOME REMARKS ON THE PERIODIC CONTINUED FRACTION", 충청수학회지, 22(2), pp.155~159 (2009), 충청수학회
- J. Paradis, "The derivative of Minkowski’s ?(x) function", J. Math. Anal. Appl, 253(1), pp.107~125 (2001)
- R. Salem, "On some singular monotonic functions which are strictly increasing", Trans. Amer. Math. Soc, 53, pp.427~439 (1943)
- P. Viader, "A new light on Minkowski’s ?(x) function", J. Number Theory, 73(2), pp.212~227 (1998)
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