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1998 | 131 | 3 | 225-251
Tytuł artykułu

$L^q$-spectrum of the Bernoulli convolution associated with the golden ratio

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Based on a set of higher order self-similar identities for the Bernoulli convolution measure for (√5-1)/2 given by Strichartz et al., we derive a formula for the $L^q$-spectrum, q >0, of the measure. This formula is the first obtained in the case where the open set condition does not hold.
Czasopismo
Rocznik
Tom
131
Numer
3
Strony
225-251
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-07-16
poprawiono
1998-04-15
Twórcy
autor
  • Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong, kslau@math.cuhk.edu.hk, lauks@pitt.edu
  • Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
autor
Bibliografia
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  • [Fe] W. Feller, An Introduction to Probability Theory and its Applications, Vol. 2, 2nd ed., Wiley, New York, 1971.
  • [FP] U. Frisch and G. Parisi, On the singularity structure of fully developed turbulence, in: Proc. Internat. School Phys., "Enrico Fermi" Course LXXXVIII, North-Holland, Amsterdam, 1985, 84-88.
  • [G] A. M. Garsia, Entropy and singularity of infinite convolutions, Pacific J. Math. 13 (1963), 1159-1169.
  • [H] T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia and B. I. Shraiman, Fractal measures and their singularities: The characterization of strange sets, Phys. Rev. A 33 (1986), 1141-1151.
  • [Hu] T. Y. Hu, The local dimensions of the Bernoulli convolution associated with the golden number, Trans. Amer. Math. Soc. 349 (1997), 2917-2940.
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  • [La] S. P. Lalley, Random series in powers of algebraic integers: Hausdorff dimension of the limit distribution, J. London Math. Soc., to appear.
  • [L1] K.-S. Lau, Fractal measures and mean p-variations, J. Funct. Anal. 108 (1992), 427-457.
  • [L2] K.-S. Lau, Dimension of a family of singular Bernoulli convolutions, ibid. 116 (1993), 335-358.
  • [LN1] K.-S. Lau and S.-M. Ngai, Multifractal measures and a weak separation condition, Adv. Math., to appear.
  • [LN2] K.-S. Lau and S.-M. Ngai, $L^q$-spectrum of Bernoulli convolutions associated with P.V. numbers, preprint.
  • [LW] K.-S. Lau and J. Wang, Mean quadratic variations and Fourier asymptotics of self-similar measures, Monatsh. Math. 115 (1993), 99-132.
  • [LP] F. Ledrappier and A. Porzio, A dimension formula for Bernoulli convolution, J. Statist. Phys. 76 (1994), 1307-1327.
  • [Lo] A. O. Lopes, The dimension spectrum of the maximal measure, SIAM J. Math. Anal. 20 (1989), 1243-1254.
  • [N] S.-M. Ngai, A dimension result arising from the $L^q$-spectrum of a measure, Proc. Amer. Math. Soc. 125 (1997), 2943-2951.
  • [O] L. Olsen, A multifractal formalism, Adv. Math. 116 (1995), 82-195.
  • [PU] F. Przytycki and M. Urbański, On the Hausdorff dimension of some fractal sets, Studia Math. 93 (1989), 155-186.
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  • [Ri] R. Riedi, An improved multifractal formalism and self-similar measures, J. Math. Anal. Appl. 189 (1995), 462-490.
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  • [St] R. S. Strichartz, Self-similar measures and their Fourier transforms III, Indiana Univ. Math. J. 42 (1993), 367-411.
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Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv131i3p225bwm
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