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Abstract:

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.

Registro:

Documento: Artículo
Título:Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images
Autor:Mosquera, C.A.; Shmerkin, P.S.
Filiación:Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Matemática, Ciudad Universitaria, Pabellón I (C1428EGA), Ciudad de Buenos Aires, Argentina
IMAS-CONICET, Argentina
Torcuato di Tella University and CONICET, Department of Mathematics and Statistics, Av. Figueroa Alcorta 7350 (C1428BCW), Ciudad de Buenos Aires, Argentina
Palabras clave:Correlation dimension; Fourier decay; Self-similar measures
Año:2018
Volumen:43
Página de inicio:823
Página de fin:834
DOI: http://dx.doi.org/10.5186/AASFM.2018.4350
Título revista:Annales Academiae Scientiarum Fennicae Mathematica
Título revista abreviado:Ann. Acad. Sci. Fenn. Math.
ISSN:1239629X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1239629X_v43_n_p823_Mosquera

Referencias:

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Citas:

---------- APA ----------
Mosquera, C.A. & Shmerkin, P.S. (2018) . Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images. Annales Academiae Scientiarum Fennicae Mathematica, 43, 823-834.
http://dx.doi.org/10.5186/AASFM.2018.4350
---------- CHICAGO ----------
Mosquera, C.A., Shmerkin, P.S. "Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images" . Annales Academiae Scientiarum Fennicae Mathematica 43 (2018) : 823-834.
http://dx.doi.org/10.5186/AASFM.2018.4350
---------- MLA ----------
Mosquera, C.A., Shmerkin, P.S. "Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images" . Annales Academiae Scientiarum Fennicae Mathematica, vol. 43, 2018, pp. 823-834.
http://dx.doi.org/10.5186/AASFM.2018.4350
---------- VANCOUVER ----------
Mosquera, C.A., Shmerkin, P.S. Self-similar measures: Asymptotic bounds for the dimension and Fourier decay of smooth images. Ann. Acad. Sci. Fenn. Math. 2018;43:823-834.
http://dx.doi.org/10.5186/AASFM.2018.4350