Abstract
Let f(x) = Σn≥1 a n cos(λnx) be a lacunary trigonomitric series with Σn≥1 |a n | < ∞. On some conditions of the coefficients a n and the frequencies λ n , we shall determine the Hausdorff dimension of its graph.
Supported partially by the Chinese National Science's Fund.
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References
M.V. Berry and Z.V. Lewis, On the Weiertrass-Mandelbrot fractal function, 1980, Pro. Roy. Soc. Lon. A370, pp459–484.
K.J.Falconer, The Geometry of fractal sets, Cam. Uni. Press, 1985.
O.Frostman, Postntiel d'équilibre et capacité des ensemble avec quelques applications á la théorie des fonctions, Meddel, Lunds Univ. Math. Sem., 3, pp1–118.
B.B. Mandelbrot, The fractal geometry of nature, San Francisco: W.H.Freeman, 1982.
R.D. Maudin and S.C. Williams, On the Hausdorff Dimension of Some Graphs, Trans. Amer. Math. Soc, Vol.298, 2, 1986, pp793–803.
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© 1991 Springer-Verlag
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Sun, Dc., Wen, Zy. (1991). The hausdorff dimension of a class of lacunary trigonomitric series. In: Cheng, MT., Deng, DG., Zhou, XW. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 1494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087769
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DOI: https://doi.org/10.1007/BFb0087769
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