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

Volume 131 / 1998

Ka-Sing Lau, Studia Mathematica 131 (1998), 225-251 DOI: 10.4064/sm-131-3-225-251


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.


  • Ka-Sing Lau

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