On the Exceptional Set for Absolute Continuity of Bernoulli Convolutions
We prove that the set of exceptional λ∈ (1/2,1) such that the associated Bernoulli convolution is singular has zero Hausdorff dimension, and likewise for biased Bernoulli convolutions, with the exceptional set independent of the bias. This improves previous results by Erdös, Kahane, Solomyak, Peres...
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Birkhauser Verlag AG
2014
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| 100 | 1 | |a Shmerkin, P. | |
| 245 | 1 | 3 | |a On the Exceptional Set for Absolute Continuity of Bernoulli Convolutions |
| 260 | |b Birkhauser Verlag AG |c 2014 | ||
| 270 | 1 | 0 | |m Shmerkin, P.; Department of Mathematics and Statistics, Torcuato Di Tella University, Av. Figueroa Alcorta 7350, 1428 Buenos Aires, Argentina; email: pshmerkin@utdt.edu |
| 506 | |2 openaire |e Política editorial | ||
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| 520 | 3 | |a We prove that the set of exceptional λ∈ (1/2,1) such that the associated Bernoulli convolution is singular has zero Hausdorff dimension, and likewise for biased Bernoulli convolutions, with the exceptional set independent of the bias. This improves previous results by Erdös, Kahane, Solomyak, Peres and Schlag, and Hochman. A theorem of this kind is also obtained for convolutions of homogeneous self-similar measures. The proofs are very short, and rely on old and new results on the dimensions of self-similar measures and their convolutions, and the decay of their Fourier transform. © 2014 Springer Basel. |l eng | |
| 536 | |a Detalles de la financiación: Leverhulme Trust | ||
| 536 | |a Detalles de la financiación: Keywords and phrases: Bernoulli convolutions, self-similar measures, hausdorff dimension Mathematics Subject Classification (1991): Primary 28A78, 28A80; Secondary 37A45 The author was supported by a Leverhulme Early Career Fellowship. | ||
| 593 | |a Department of Mathematics and Statistics, Torcuato Di Tella University, Av. Figueroa Alcorta 7350, 1428 Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a 28A80 |
| 690 | 1 | 0 | |a BERNOULLI CONVOLUTIONS |
| 690 | 1 | 0 | |a HAUSDORFF DIMENSION |
| 690 | 1 | 0 | |a PRIMARY 28A78 |
| 690 | 1 | 0 | |a SECONDARY 37A45 |
| 690 | 1 | 0 | |a SELF-SIMILAR MEASURES |
| 773 | 0 | |d Birkhauser Verlag AG, 2014 |g v. 24 |h pp. 946-958 |k n. 3 |p Geom. Funct. Anal. |x 1016443X |t Geometric and Functional Analysis | |
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| 856 | 4 | 0 | |u https://doi.org/10.1007/s00039-014-0285-4 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_1016443X_v24_n3_p946_Shmerkin |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1016443X_v24_n3_p946_Shmerkin |y Registro en la Biblioteca Digital |
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