Absolute continuity of non-homogeneous self-similar measures
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2017
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| _version_ | 1866914953903996928 |
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| author | Saglietti, Santiago Shmerkin, Pablo Solomyak, Boris |
| author_facet | Saglietti, Santiago Shmerkin, Pablo Solomyak, Boris |
| contents | We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S-M. Ngai and Y. Wang. While recently there has been much progress in understanding absolute continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case. In the course of the proof, we establish new results on the dimension and Fourier decay of a class of random self-similar measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1709_05092 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Absolute continuity of non-homogeneous self-similar measures Saglietti, Santiago Shmerkin, Pablo Solomyak, Boris Dynamical Systems Classical Analysis and ODEs Probability 28A78, 28A80 (Primary) 37A45, 42A38 (secondary) We prove that self-similar measures on the real line are absolutely continuous for almost all parameters in the super-critical region, in particular confirming a conjecture of S-M. Ngai and Y. Wang. While recently there has been much progress in understanding absolute continuity for homogeneous self-similar measures, this is the first improvement over the classical transversality method in the general (non-homogeneous) case. In the course of the proof, we establish new results on the dimension and Fourier decay of a class of random self-similar measures. |
| title | Absolute continuity of non-homogeneous self-similar measures |
| topic | Dynamical Systems Classical Analysis and ODEs Probability 28A78, 28A80 (Primary) 37A45, 42A38 (secondary) |
| url | https://arxiv.org/abs/1709.05092 |