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Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures

100%

Lau K.-S., Wang J.-R., Chu C.-H.

Studia Mathematica

1995-1996

tom 117

nr 1

1-28

The Choquet-Deny theorem and Deny's theorem are extended to the vector-valued case. They are applied to give a simple nonprobabilistic proof of the vector-valued renewal theorem, which is used to study the $L^p$-dimension, the $L^p$-density and the Fourier transformation of vector-valued self-similar measures. The results answer some questions raised by Strichartz.

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

84%

Lau K.-S., Ngai S.-M.

Studia Mathematica

1998

tom 131

nr 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.

Ograniczanie wyników

2 Studia Mathematica

2 Lau K.-S.

1 Chu C.-H.

1 Ngai S.-M.

1 Wang J.-R.

1 1998

1 1995

Wyniki wyszukiwania

Vector-valued Choquet-Deny theorem, renewal equation and self-similar measures

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