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

Ka-Sing Lau; Sze-Man Ngai

Studia Mathematica (1998)

  • Volume: 131, Issue: 3, page 225-251
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Lau, Ka-Sing, and Ngai, Sze-Man. "$L^q$-spectrum of the Bernoulli convolution associated with the golden ratio." Studia Mathematica 131.3 (1998): 225-251. <http://eudml.org/doc/216578>.

@article{Lau1998,
abstract = {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.},
author = {Lau, Ka-Sing, Ngai, Sze-Man},
journal = {Studia Mathematica},
keywords = {Bernoulli convolution; golden ratio; multifractal measure; $L^q$-spectrum; $L^q$-dimension; Hausdorff dimension; renewal equation; self-similarity; -spectrum; -dimension},
language = {eng},
number = {3},
pages = {225-251},
title = {$L^q$-spectrum of the Bernoulli convolution associated with the golden ratio},
url = {http://eudml.org/doc/216578},
volume = {131},
year = {1998},
}

TY - JOUR
AU - Lau, Ka-Sing
AU - Ngai, Sze-Man
TI - $L^q$-spectrum of the Bernoulli convolution associated with the golden ratio
JO - Studia Mathematica
PY - 1998
VL - 131
IS - 3
SP - 225
EP - 251
AB - 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.
LA - eng
KW - Bernoulli convolution; golden ratio; multifractal measure; $L^q$-spectrum; $L^q$-dimension; Hausdorff dimension; renewal equation; self-similarity; -spectrum; -dimension
UR - http://eudml.org/doc/216578
ER -

References

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