info:eu-repo/semantics/article
Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images
Fecha
2018-02Registro en:
Mosquera, Carolina Alejandra; Shmerkin, Pablo Sebastian; Self-similar measures: asymptotic bounds for the dimension and Fourier decay of smooth images; Suomalainen Tiedeakatemia; Annales Academiae Scientiarum Fennicae. Mathematica; 43; 2; 2-2018; 823-834
1239-629X
1798-2383
CONICET Digital
CONICET
Autor
Mosquera, Carolina Alejandra
Shmerkin, Pablo Sebastian
Resumen
R. Kaufman and M. Tsujii proved that the Fourier transform of self-similar measures has a power decay outside of a sparse set of frequencies. We present a version of this result for homogeneous self-similar measures, with quantitative estimates, and derive several applications: (1) non-linear smooth images of homogeneous self-similar measures have a power Fourier decay, (2) convolving with a homogeneous self-similar measure increases correlation dimension by a quantitative amount, (3) the dimension and Frostman exponent of (biased) Bernoulli convolutions tend to 1 as the contraction ratio tends to 1, at an explicit quantitative rate.