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

Studia Mathematica (1998)

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

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topLau, 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 -

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