Lq-spectrum of the Bernoulli convolution associated with the golden ratio

Ka Sing Lau; Sze Man Ngai

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

Ka Sing Lau, Sze Man Ngai

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

53 Scopus citations

Abstract

Based on a set of higher order self-similar identifications 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 is the first set of condition that does not hold.

Original language	English
Pages (from-to)	225-251
Number of pages	27
Journal	Studia Mathematica
Volume	131
Issue number	3
State	Published - 1998

Scopus Subject Areas

General Mathematics

Keywords

Bernoulli convolution
Golden ratio
Hausdorff dimension
L-dimension
L-spectrum
Multifractal measure
Renewal equation
Self-similarity

Cite this

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title = "Lq-spectrum of the Bernoulli convolution associated with the golden ratio",

abstract = " Based on a set of higher order self-similar identifications 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 is the first set of condition that does not hold. ",

keywords = "Bernoulli convolution, Golden ratio, Hausdorff dimension, L-dimension, L-spectrum, Multifractal measure, Renewal equation, Self-similarity",

author = "Lau, \{Ka Sing\} and Ngai, \{Sze Man\}",

note = "Conference on functional analysis (September 4-10, 1960, Warsaw) S. Mazur Studia Mathematica (1963), 1-6 DOI: 10.4064/sm-Special Series-1-1-6",

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AU - Lau, Ka Sing

AU - Ngai, Sze Man

N1 - Conference on functional analysis (September 4-10, 1960, Warsaw) S. Mazur Studia Mathematica (1963), 1-6 DOI: 10.4064/sm-Special Series-1-1-6

PY - 1998

Y1 - 1998

N2 - Based on a set of higher order self-similar identifications 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 is the first set of condition that does not hold.

AB - Based on a set of higher order self-similar identifications 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 is the first set of condition that does not hold.

KW - Bernoulli convolution

KW - Golden ratio

KW - Hausdorff dimension

KW - L-dimension

KW - L-spectrum

KW - Multifractal measure

KW - Renewal equation

KW - Self-similarity

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M3 - Article

SN - 0039-3223

VL - 131

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JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

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

Abstract

Scopus Subject Areas

Keywords

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