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

• Autorzy: Ka-Sing Lau , Sze-Man Ngai
• 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.

Słowa kluczowe

EN

Bernoulli convolution; golden ratio; multifractal measure; $L^q$-spectrum; $L^q$-dimension; Hausdorff dimension; renewal equation; self-similarity

Kategorie tematyczne

• 28A78: Hausdorff and packing measures
• 28A80: Fractals

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 131
• Numer: 3
• Strony: 225-251

Daty

wydano

1998

otrzymano

1997-07-16

poprawiono

1998-04-15

Twórcy

autor

Ka-Sing Lau

• Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong
• Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.

autor

Sze-Man Ngai

• Department of Mathematics, Cornell University, Ithaca, New York 14853 U.S.A.

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