Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images
Kaufman and 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 image...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_1239629X_v43_n_p823_Mosquera |
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todo:paper_1239629X_v43_n_p823_Mosquera2023-10-03T16:09:12Z Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images Mosquera, C.A. Shmerkin, P.S. Correlation dimension Fourier decay Self-similar measures Kaufman and 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. © 2018, Annales Academiæ Scientiarum Fennicæ Mathematica. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_1239629X_v43_n_p823_Mosquera |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Correlation dimension Fourier decay Self-similar measures |
| spellingShingle |
Correlation dimension Fourier decay Self-similar measures Mosquera, C.A. Shmerkin, P.S. Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images |
| topic_facet |
Correlation dimension Fourier decay Self-similar measures |
| description |
Kaufman and 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. © 2018, Annales Academiæ Scientiarum Fennicæ Mathematica. |
| format |
JOUR |
| author |
Mosquera, C.A. Shmerkin, P.S. |
| author_facet |
Mosquera, C.A. Shmerkin, P.S. |
| author_sort |
Mosquera, C.A. |
| title |
Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images |
| title_short |
Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images |
| title_full |
Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images |
| title_fullStr |
Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images |
| title_full_unstemmed |
Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images |
| title_sort |
self-similar measures: asymptotic bounds for the dimension and fourier decay of smooth images |
| url |
http://hdl.handle.net/20.500.12110/paper_1239629X_v43_n_p823_Mosquera |
| work_keys_str_mv |
AT mosqueraca selfsimilarmeasuresasymptoticboundsforthedimensionandfourierdecayofsmoothimages AT shmerkinps selfsimilarmeasuresasymptoticboundsforthedimensionandfourierdecayofsmoothimages |
| _version_ |
1807320339432079360 |