For random Bernoulli convolutions, the Fourier transform is in L^1 almost surely whenever λ_g > 2/π, giving absolute continuity and non-empty interior; polynomial Fourier decay holds for every λ_g.
Smoothness of random self-similar measures on the line and the existence of interior points
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
In this paper, we study the smoothness of the density function of absolutely continuous measures supported on random self-similar sets on the line. We show that the natural projection of a measure with symbolic local dimension greater than 1 at every point is absolutely continuous with H\"older continuous density almost surely. In particular, if the similarity dimension is greater than 1 then the random self-similar set on the line contains an interior point almost surely.
fields
math.DS 1years
2025 1verdicts
ACCEPT 1representative citing papers
citing papers explorer
-
On the Fourier transform of random Bernoulli convolutions
For random Bernoulli convolutions, the Fourier transform is in L^1 almost surely whenever λ_g > 2/π, giving absolute continuity and non-empty interior; polynomial Fourier decay holds for every λ_g.