Abstract
Our study is of the Hausdorff dimension and the packing dimension of graphs of Rademacher series whose coefficients form geometric progression.
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References
W.A. Beyer, Hausdorff dimension of level sets of some Rademacher series. Pacific J. Math.,12(1962), 35–46.
D.W. Boyd, The distribution of the Pisot numbers in the real line. Séminaire de Théorie des Nombres, Paris 1983–84, Birkhäuser Boston Inc., Boston, 1985, 9–23.
G. de Rham, Sur quelques courbes définites par des équations fonctionnelles. Rend. Sem. Mat. Torino,16(1957), 101–113.
P. Erdös, On a family of symmetric Bernoulli convolutions. Amer. J. Math.,61(1939), 974–976.
K.J. Falconer, The Geometry of Fractal Sets. Cambridge University, Press, Cambridge, 1985.
A.M. Garsia, Arithmetic properties of Bernoulli convolutions. Trans. Amer. Math. Soc.,102(1962), 409–432.
M. Hata and M. Yamaguti, The Takagi function and its generalization. Japan J. Appl. Math.1(1984), 183–199.
N. Kôno, On self-affine functions. Japan J. Appl. Math.,3(1986), 259–269.
B.B. Mandelbrot, The Fractal Geometry of Nature. W.H. Freeman and Co., San Francisco, 1982.
F. Przytycki and M. Urbański, On Hausdorff dimension of some fractal sets. Studia Math.,93(1989), 155–186.
R. Salem, On some singular monotonic functions which are strictly increasing. Trans. Amer. Math. Soc.,53(1943), 427–439.
S.J. Taylor, and C. Tricot, Packing measure and its evaluation for a Brownian path. Trans. Amer. Math. Soc.,288(1985), 679–699.
C. Tricot, Dimensions de graphes. C. R. Acad. Sci. Paris,303(1986), 609–612.
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Shiota, Y., Sekiguchi, T. Hausdorff dimension of graphs of some Rademacher series. Japan J. Appl. Math. 7, 121–129 (1990). https://doi.org/10.1007/BF03167894
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DOI: https://doi.org/10.1007/BF03167894