A generalization of Hata-Yamaguti's results on the Takagi function II: Multinomial case

Japan Journal of Industrial and Applied Mathematics

Volumn 13, Issue 3, 1996, Pages 435-463

  Okada, Tatsuya ^a   Sekiguchi, Takeshi ^b   Shiota, Yasunobu ^b,c  

^a FUKUSHIMA MEDICAL UNIVERSITY   (Japan)

^b TOHOKU GAKUIN UNIVERSITY   (Japan)

^c AKITA UNIVERSITY   (Japan)

Author keywords

Difference equation; Martingale; Multinomial measure; Schauder expansion; Takagi function

Indexed keywords

EID: 0038889847     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167257     Document Type: Article

References (18)

1. G. de Rham, Sur quelques courbes définies par des équations fonctionnelles. Rend. Sem. Mat. Torino, 16 (1957), 101-113.
2. K. J. Falconer, Fractal Geometry. John Wiley, 1990.
3. M. Hata, On the structure of self-similar sets. Japan J. Appl. Math., 2 (1985), 381-414.
4. M. Hata and M. Yamaguti, The Takagi function and its generalization. Japan J. Appl. Math., 1 (1984), 183-199.
5. S. Kakutani, On equivalence of infinite product measures. Ann. of Math., 49 (1948), 214-224.
6. J. Kigami, Harmonic analysis on the Sierpinski gasket. Japan J. Appl. Math., 6 (1989), 259-290.
7. J. Kigami, Harmonic analysis on P.C.F. self-similar sets. Trans. Amer. Math. Soc., 335 (1993), 721-755.
8. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis. 1, Graylock, Rochester, 1957, 99.
9. N. Kôno, On self-affine functions. Japan J. Appl. Math., 3 (1986), 259-269.
10. N. Kôno, On self-affine functions II. Japan J. Appl. Math., 5 (1988), 441-454.
11. K. Muramoto, T. Okada, T. Sekiguchi and Y. Shiota, Digital sum problems for the p-adic expansion of positive integers. In preparation.
12. T. Okada, T. Sekiguchi and Y. Shiota, Applications of binomial measures to power sums of digital sums. J. Number Theory, 52 (1995), 256-266.
13. T. Okada, T. Sekiguchi and Y. Shiota, Explicit formulas of exponential sums of digital sums. Japan J. Indust. Appl. Math., 12 (1995), 425-438.
14. R. Salem, On some singular monotonic functions which are strictly increasing. Trans. Amer. Math. Soc., 53 (1943), 427-439.
15. T. Sekiguchi and Y. Shiota, A generalization of Hata-Yamaguti's results on the Takagi function. Japan J. Indust. Appl. Math., 8 (1991), 203-219.
16. Y. Shiota, Remarks on self-similarity. Japan J. Appl. Math., 7 (1990), 171-181.
17. T. Takagi, A simple example of the continuous function without derivative. The Collected Papers of Teiji Takagi, Iwanami Shoten, 1973, 5-6.
18. M. Yamaguti, M. Hata and J. Kigami, Mathematics on Fractal. Iwanami Shoten, 1993. (In Japanese)